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<h3>References</h3>


<p><a id="biBlrslib" name="biBlrslib"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Avi</span>]   <b class='BibAuthor'>Avis, D.</b>,
 <i class='BibTitle'>lrslib -- reverse search vertex enumeration program</i>,
<span class='BibHowpublished'>{A}vailable at
      \url{https://cgm.cs.mcgill.ca/~avis/C/lrs.html}</span>.
</p>


<p><a id="biBBaCa" name="biBBaCa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BC17</span>]   <b class='BibAuthor'>B\"achle, A. and Caicedo, M.,
 <i class='BibTitle'>On the prime graph question for almost simple groups with an
              alternating socle</i>,
 <span class='BibJournal'>Internat. J. Algebra Comput.</span>,
 <em class='BibVolume'>27</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'>333--347</span>.
</p>


<p><a id="biBBovdiHertweck" name="biBBovdiHertweck"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BH08</span>]   <b class='BibAuthor'>Bovdi, V. A. and Hertweck, M.</b>,
 <i class='BibTitle'>Zassenhaus conjecture for central extensions of
      S_5</i>,
 <span class='BibJournal'>J. Group Theory</span>,
 <em class='BibVolume'>11</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>63--74</span>.
</p>


<p><a id="biBBaHeKoMaSi" name="biBBaHeKoMaSi"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BHK+18</span>]   <b class='BibAuthor'>B\"{a}chle, A., Herman, A., Konovalov, A., Margolis, L. and Singh, G.,
 <i class='BibTitle'>The status of the Zassenhaus conjecture for small
      groups</i>,
 <span class='BibJournal'>Exp. Math.</span>,
 <em class='BibVolume'>27</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>431--436</span>.
</p>


<p><a id="biBNormaliz" name="biBNormaliz"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BIR+</span>]   <b class='BibAuthor'>Bruns, W., Ichim, B., R\"omer, T., Sieg, R. and S\"oger, C.</b>,
 <i class='BibTitle'>Normaliz. Algorithms for rational cones and affine monoids</i>,
<span class='BibHowpublished'>Available at \url{https://normaliz.uos.de}</span>.
</p>


<p><a id="biBBJK" name="biBBJK"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BJK11</span>]   <b class='BibAuthor'>Bovdi, V. A., Jespers, E. and Konovalov, A. B.</b>,
 <i class='BibTitle'>Torsion units in integral group rings of Janko simple
              groups</i>,
 <span class='BibJournal'>Math. Comp.</span>,
 <em class='BibVolume'>80</em> (<span class='BibNumber'>273</span>)
 (<span class='BibYear'>2011</span>),
 <span class='BibPages'>593--615</span>.
</p>


<p><a id="biBKonovalovM11" name="biBKonovalovM11"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BK07a</span>]   <b class='BibAuthor'>Bovdi, V. A. and Konovalov, A. B.</b>,
 <i class='BibTitle'>Integral group ring of the first Mathieu simple group</i>,
  in  <i class='BibBooktitle'>Groups St. Andrews 2005. Vol. 1</i>,
 <span class='BibPublisher'>Cambridge Univ. Press, Cambridge</span>,
 <span class='BibSeries'>London Math. Soc. Lecture Note Ser.</span>,
 <em class='BibVolume'>339</em>
 (<span class='BibYear'>2007</span>),
 <span class='BibPages'>237--245</span>.
</p>


<p><a id="biBKonovalovMcL" name="biBKonovalovMcL"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BK07b</span>]   <b class='BibAuthor'>Bovdi, V. A. and Konovalov, A. B.</b>,
 <i class='BibTitle'>Integral group ring of the McLaughlin simple
      group</i>,
 <span class='BibJournal'>Algebra Discrete Math.</span> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2007</span>),
 <span class='BibPages'>43--53</span>.
</p>


<p><a id="biBBKHS" name="biBBKHS"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BK10</span>]   <b class='BibAuthor'>Bovdi, V. A. and Konovalov, A. B.</b>,
 <i class='BibTitle'>Torsion units in integral group ring of Higman-Sims
      simple
              group</i>,
 <span class='BibJournal'>Studia Sci. Math. Hungar.</span>,
 <em class='BibVolume'>47</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>1--11</span>.
</p>


<p><a id="biBKonovalovM22" name="biBKonovalovM22"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BKL08</span>]   <b class='BibAuthor'>Bovdi, V. A., Konovalov, A. B. and Linton, S.</b>,
 <i class='BibTitle'>Torsion units in integral group ring of the Mathieu simple
              group M_22</i>,
 <span class='BibJournal'>LMS J. Comput. Math.</span>,
 <em class='BibVolume'>11</em>
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>28--39</span>.
</p>


<p><a id="biBBachleKimmerleSerrano" name="biBBachleKimmerleSerrano"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BKS20</span>]   <b class='BibAuthor'>B\"{a}chle, A., Kimmerle, W. and Serrano, M.,
 <i class='BibTitle'>On the first Zassenhaus conjecture and direct products</i>,
 <span class='BibJournal'>Canad. J. Math.</span>,
 <em class='BibVolume'>72</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2020</span>),
 <span class='BibPages'>602--624</span>.
</p>


<p><a id="biBBaMa4prI" name="biBBaMa4prI"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM17a</span>]   <b class='BibAuthor'>B\"achle, A. and Margolis, L.,
 <i class='BibTitle'>On the prime graph question for integral group rings of
              4-primary groups I</i>,
 <span class='BibJournal'>Internat. J. Algebra Comput.</span>,
 <em class='BibVolume'>27</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'>731--767</span>.
</p>


<p><a id="biBBaMaM10" name="biBBaMaM10"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM17b</span>]   <b class='BibAuthor'>B\"achle, A. and Margolis, L.,
 <i class='BibTitle'>Rational conjugacy of torsion units in integral group rings of
              non-solvable groups</i>,
 <span class='BibJournal'>Proc. Edinb. Math. Soc. (2)</span>,
 <em class='BibVolume'>60</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'>813--830</span>.
</p>


<p><a id="biBBaMaHeLPArticle" name="biBBaMaHeLPArticle"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM18</span>]   <b class='BibAuthor'>B\"achle, A. and Margolis, L.,
 <i class='BibTitle'>HeLP: a GAP package for torsion units in integral group
              rings</i>,
 <span class='BibJournal'>J. Softw. Algebra Geom.</span>,
 <em class='BibVolume'>8</em>
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>1--9</span>.
</p>


<p><a id="biBBaMaAn" name="biBBaMaAn"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM19a</span>]   <b class='BibAuthor'>B\"{a}chle, A. and Margolis, L.,
 <i class='BibTitle'>An application of blocks to torsion units in group rings</i>,
 <span class='BibJournal'>Proc. Amer. Math. Soc.</span>,
 <em class='BibVolume'>147</em> (<span class='BibNumber'>10</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>4221--4231</span>.
</p>


<p><a id="biBBaMa4prII" name="biBBaMa4prII"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM19b</span>]   <b class='BibAuthor'>B\"{a}chle, A. and Margolis, L.,
 <i class='BibTitle'>On the prime graph question for integral group rings of
              4-primary groups II</i>,
 <span class='BibJournal'>Algebr. Represent. Theory</span>,
 <em class='BibVolume'>22</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>437--457</span>.
</p>


<p><a id="biBBachleMargolisExamplesToMethods" name="biBBachleMargolisExamplesToMethods"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BM21</span>]   <b class='BibAuthor'>B\"{a}chle, A. and Margolis, L.,
 <i class='BibTitle'>From examples to methods: two cases from the study of units in
              integral group rings</i>,
 <span class='BibJournal'>Indian J. Pure Appl. Math.</span>,
 <em class='BibVolume'>52</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>669--686</span>.
</p>


<p><a id="biBCaicedoDelRio20" name="biBCaicedoDelRio20"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CdR20</span>]   <b class='BibAuthor'>Caicedo, M. and del R\'{\i}o, \.,
 <i class='BibTitle'>On the Zassenhaus conjecture for certain cyclic-by-nilpotent
              groups</i>,
 <span class='BibJournal'>Mediterr. J. Math.</span>,
 <em class='BibVolume'>17</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2020</span>),
 <span class='BibPages'>Paper No. 62, 17</span>.
</p>


<p><a id="biBCohnLivingstone" name="biBCohnLivingstone"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CL65</span>]   <b class='BibAuthor'>Cohn, J. A. and Livingstone, D.</b>,
 <i class='BibTitle'>On the structure of group algebras. I</i>,
 <span class='BibJournal'>Canad. J. Math.</span>,
 <em class='BibVolume'>17</em>
 (<span class='BibYear'>1965</span>),
 <span class='BibPages'>583--593</span>.
</p>


<p><a id="biBCaMaBrauerTree" name="biBCaMaBrauerTree"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CM21</span>]   <b class='BibAuthor'>Caicedo, M. and Margolis, L.</b>,
 <i class='BibTitle'>Orders of units in integral group rings and blocks of defect
              1</i>,
 <span class='BibJournal'>J. Lond. Math. Soc. (2)</span>,
 <em class='BibVolume'>103</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>1515--1546</span>.
</p>


<p><a id="biBCyclicByAbelian" name="biBCyclicByAbelian"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CMdR13</span>]   <b class='BibAuthor'>Caicedo, M., Margolis, L. and del R{\'{\i}}o, {.,
 <i class='BibTitle'>Zassenhaus conjecture for cyclic-by-abelian groups</i>,
 <span class='BibJournal'>J. Lond. Math. Soc. (2)</span>,
 <em class='BibVolume'>88</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>65--78</span>.
</p>


<p><a id="biBCR1" name="biBCR1"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CR90</span>]   <b class='BibAuthor'>Curtis, C. W. and Reiner, I.</b>,
 <i class='BibTitle'>Methods of representation theory. Vol. I</i>,
 <span class='BibPublisher'>John Wiley \& Sons, Inc., New York</span>,
 <span class='BibSeries'>Wiley Classics Library</span>
 (<span class='BibYear'>1990</span>),
 <span class='BibPages'>xxiv+819 pages</span><br />
(<span class='BibNote'>With applications to finite groups and orders,
              Reprint of the 1981 original,
              A Wiley-Interscience Publication</span>).
</p>


<p><a id="biBdelRioSerrano19" name="biBdelRioSerrano19"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>dRS19</span>]   <b class='BibAuthor'>del R\'{\i}o, \. and Serrano, M.,
 <i class='BibTitle'>Zassenhaus conjecture on torsion units holds for SL(2,p) and SL(2,p^2)</i>,
 <span class='BibJournal'>J. Group Theory</span>,
 <em class='BibVolume'>22</em> (<span class='BibNumber'>5</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>953--974</span>.
</p>


<p><a id="biBEiMa18" name="biBEiMa18"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EM18</span>]   <b class='BibAuthor'>Eisele, F. and Margolis, L.</b>,
 <i class='BibTitle'>A counterexample to the first Zassenhaus conjecture</i>,
 <span class='BibJournal'>Adv. Math.</span>,
 <em class='BibVolume'>339</em>
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>599--641</span>.
</p>


<p><a id="biBEiseleMargolisDefect1" name="biBEiseleMargolisDefect1"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EM22</span>]   <b class='BibAuthor'>Eisele, F. and Margolis, L.</b>,
 <i class='BibTitle'>Units in blocks of defect 1 and the Zassenhaus Conjecture</i>,
 <span class='BibJournal'>preprint, arxiv.org/abs/arXiv:2212.06634</span>
 (<span class='BibYear'>2022</span>),
 <span class='BibPages'>29 pages</span>.
</p>


<p><a id="biBGildea" name="biBGildea"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gil13</span>]   <b class='BibAuthor'>Gildea, J.</b>,
 <i class='BibTitle'>Zassenhaus conjecture for integral group ring of simple linear
              groups</i>,
 <span class='BibJournal'>J. Algebra Appl.</span>,
 <em class='BibVolume'>12</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>1350016, 10</span>.
</p>


<p><a id="biBHertweckColloq" name="biBHertweckColloq"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Her06</span>]   <b class='BibAuthor'>Hertweck, M.</b>,
 <i class='BibTitle'>On the torsion units of some integral group rings</i>,
 <span class='BibJournal'>Algebra Colloq.</span>,
 <em class='BibVolume'>13</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>329--348</span>.
</p>


<p><a id="biBHertweckBrauer" name="biBHertweckBrauer"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Her07</span>]   <b class='BibAuthor'>Hertweck, M.</b>,
 <i class='BibTitle'>Partial Augmentations and Brauer Character values of torion
      Units in Group Rings</i>,
 <span class='BibJournal'>Preprint</span>
 (<span class='BibYear'>2007</span>)<br />
(<span class='BibNote'>e-print
      \href{https://arxiv.org/abs/math/0612429v2}{\nolinkurl{arXiv:math.RA/0612429v2
      [math.RA]}}</span>).
</p>


<p><a id="biBHertweckSolvable" name="biBHertweckSolvable"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Her08a</span>]   <b class='BibAuthor'>Hertweck, M.</b>,
 <i class='BibTitle'>The orders of torsion units in integral group rings of finite
              solvable groups</i>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>36</em> (<span class='BibNumber'>10</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>3585--3588</span>.
</p>


<p><a id="biBHertweckEdinb" name="biBHertweckEdinb"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Her08b</span>]   <b class='BibAuthor'>Hertweck, M.</b>,
 <i class='BibTitle'>Torsion units in integral group rings of certain metabelian
              groups</i>,
 <span class='BibJournal'>Proc. Edinb. Math. Soc. (2)</span>,
 <em class='BibVolume'>51</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>363--385</span>.
</p>


<p><a id="biBHerA6" name="biBHerA6"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Her08c</span>]   <b class='BibAuthor'>Hertweck, M.</b>,
 <i class='BibTitle'>Zassenhaus conjecture for A_6</i>,
 <span class='BibJournal'>Proc. Indian Acad. Sci. Math. Sci.</span>,
 <em class='BibVolume'>118</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>189--195</span>.
</p>


<p><a id="biBHoefertKimmerle" name="biBHoefertKimmerle"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>HK06</span>]   <b class='BibAuthor'>H{\"o}fert, C. and Kimmerle, W.,
 <i class='BibTitle'>On torsion units of integral group rings of groups of small
              order</i>,
  in  <i class='BibBooktitle'>Groups, rings and group rings</i>,
 <span class='BibPublisher'>Chapman \& Hall/CRC, Boca Raton, FL</span>,
 <span class='BibSeries'>Lect. Notes Pure Appl. Math.</span>,
 <em class='BibVolume'>248</em>
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>243--252</span>.
</p>


<p><a id="biBJuriaansMilies" name="biBJuriaansMilies"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>JPM00</span>]   <b class='BibAuthor'>Juriaans, S. O. and Polcino Milies, C.</b>,
 <i class='BibTitle'>Units of integral group rings of Frobenius groups</i>,
 <span class='BibJournal'>J. Group Theory</span>,
 <em class='BibVolume'>3</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2000</span>),
 <span class='BibPages'>277--284</span>.
</p>


<p><a id="biBKimmiPQ" name="biBKimmiPQ"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kim06</span>]   <b class='BibAuthor'>Kimmerle, W.</b>,
 <i class='BibTitle'>On the prime graph of the unit group of integral group rings
              of finite groups</i>,
  in  <i class='BibBooktitle'>Groups, rings and algebras</i>,
 <span class='BibPublisher'>Amer. Math. Soc., Providence, RI</span>,
 <span class='BibSeries'>Contemp. Math.</span>,
 <em class='BibVolume'>420</em>
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>215--228</span>.
</p>


<p><a id="biBAri" name="biBAri"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kim07</span>]   <b class='BibAuthor'>Kimmerle, W.</b>,
 <i class='BibTitle'>Mini-Workshop: Arithmetik von
      Gruppenringen</i>,
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[<span class='BibKey'>KK15</span>]   <b class='BibAuthor'>Kimmerle, W. and Konovalov, A. B.</b>,
 <i class='BibTitle'>Recent advances on torsion subgroups of Integral Group
      Rings</i>,
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[<span class='BibKey'>MdR19</span>]   <b class='BibAuthor'>Margolis, L. and del R\'{\i}o, \.,
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              conjecture related problem</i>,
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[<span class='BibKey'>MdRS19</span>]   <b class='BibAuthor'>Margolis, L., del R\'{\i}o, \. and Serrano, M.,
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      Mathematics</span>,
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              combinatorial problems on linear spaces</i>,
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[<span class='BibKey'>Wei91</span>]   <b class='BibAuthor'>Weiss, A.</b>,
 <i class='BibTitle'>Torsion units in integral group rings</i>,
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 <i class='BibTitle'>On the torsion units of group rings</i>,
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      Instituto de Alta Cultura (Portugese)</span>
 (<span class='BibYear'>1974</span>),
 <span class='BibPages'>119-126</span>.
</p>

<p> </p>


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