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<entry id="Andaloro00"><article>
  <author>
    <name><first>P.</first><last>Andaloro</last></name>
  </author>
  <title>On Total Stopping Times under <M>3x+1</M> Iteration</title>
  <journal>Fibonacci Quarterly</journal>
  <year>2000</year>
  <volume>38</volume>
  <pages>73-78</pages>
  <mrnumber>1738650 (2000m:11024)</mrnumber>
</article></entry>

<entry id="BhattacharjeeMacphersonMoellerNeumann98"><book>
  <author>
    <name><first>Meenaxi</first><last>Bhattacharjee</last></name>
    <name><first>Dugald</first><last>Macpherson</last></name>
    <name><first>Rögnvaldur G.</first><last>Möller</last></name>
    <name><first>Peter M.</first><last>Neumann</last></name>
  </author>
  <title>Notes on Infinite Permutation Groups</title>
  <publisher>Springer-Verlag</publisher>
  <year>1998</year>
  <number>1698</number>
  <series>Lecture Notes in Mathematics</series>
  <isbn>3-540-64965-4</isbn>
  <mrnumber>1632579 (99e:20003)</mrnumber>
</book></entry>

<entry id="DixonMortimer96"><book>
  <author>
    <name><first>John D.</first><last>Dixon</last></name>
    <name><first>Brian</first><last>Mortimer</last></name>
  </author>
  <title>Permutation Groups</title>
  <publisher>Springer-Verlag</publisher>
  <year>1996</year>
  <number>163</number>
  <series>Graduate Texts in Mathematics</series>
  <isbn>0-387-94599-7</isbn>
  <mrnumber>1409812 (98m:20003)</mrnumber>
</book></entry>

<entry id="Farkas04"><inproceedings>
  <author>
    <name><first>H. M.</first><last>Farkas</last></name>
  </author>
  <title>Variants of the <M>3n+1</M> Problem and Multiplicative Semigroups</title>
  <booktitle>Proc. Robert Brooks Memorial Conference</booktitle>
  <year>2004</year>
  <series>Contemp. Math.</series>
  <publisher>Amer. Math. Soc.</publisher>
</inproceedings></entry>

<entry id="FR"><manual>
  <author>
    <name><first>Laurent</first><last>Bartholdi</last></name>
  </author>
  <title>
    <C>FR -- Computations with functionally recursive groups. Version 2.2.1</C>
  </title>
  <year>2015</year>
  <other type="note">
    GAP package, <URL>https://www.gap-system.org/Packages/fr.html</URL>
  </other>
</manual></entry>

<entry id="Fuerstenberg55"><article>
  <author>
    <name><first>Harry</first><last>Fürstenberg</last></name>
  </author>
  <title>On the Infinitude of Primes</title>
  <journal>Amer. Math. Monthly</journal>
  <year>1955</year>
  <volume>62</volume>
  <pages>353</pages>
  <mrnumber>0068566 (16,904e)</mrnumber>
</article></entry>

<entry id="GAPDoc"><manual>
  <author>
    <name><first>Frank</first><last>Lübeck</last></name>
    <name><first>Max</first><last>Neunhöffer</last></name>
  </author>
  <title><C>GAPDoc (Version 1.5.1)</C></title>
  <organization>RWTH Aachen</organization>
  <year>2012</year>
  <other type="note">
    GAP package, <URL>https://www.gap-system.org/Packages/gapdoc.html</URL>
  </other>
</manual></entry>

<entry id="GluckTaylor02"><article>
  <author>
    <name><first>David</first><last>Gluck</last></name>
    <name><first>Brian D.</first><last>Taylor</last></name>
  </author>
  <title>A New Statistic for the <M>3x+1</M> Problem</title>
  <journal>Proc. Amer. Math. Soc.</journal>
  <year>2002</year>
  <volume>130</volume>
  <number>5</number>
  <pages>1293-1301</pages>
  <mrnumber>1879950 (2002k:11031)</mrnumber>
</article></entry>

<entry id="GRAPE"><manual>
  <author>
    <name><first>Leonard</first><last>Soicher</last></name>
  </author>
  <title><C>GRAPE -- GRaph Algorithms using PErmutation groups (Version 4.7)</C></title>
  <organization>Queen Mary, University of London</organization>
  <year>2016</year>
  <other type="note">
    GAP package, <URL>https://www.gap-system.org/Packages/grape.html</URL>
  </other>
</manual></entry>

<entry id="GreenTao04"><misc>
  <author>
    <name><first>Ben</first><last>Green</last></name>
    <name><first>Terence</first><last>Tao</last></name>
  </author>
  <title>
    The Primes Contain Arbitrarily Long Arithmetic Progressions
  </title>
  <year>2004</year>
  <note><URL>https://arxiv.org/abs/math.NT/0404188v1</URL></note>
</misc></entry>

<entry id="Grigorchuk80"><article>
  <author>
    <name><first>Rostislav I.</first><last>Grigorchuk</last></name>
  </author>
  <title>Burnside's Problem on Periodic Groups
  <journal>Functional Anal. Appl.</journal>
  <year>1980</year>
  <volume>14</volume>
  <pages>41-43</pages>
  <mrnumber>0565099 (81m:20045)</mrnumber>
</article></entry>

<entry id="HicksMullenYucasZavislak08"><article>
  <author>
    <name><first>Kenneth</first><last>Hicks</last></name>
    <name><first>Gary L.</first><last>Mullen</last></name>
    <name><first>Joseph L.</first><last>Yucas</last></name>
    <name><first>Ryan</first><last>Zavislak</last></name>
  </author>
  <title>A Polynomial Analogue of the <M>3n+1</M> Problem</title>
  <journal>Amer. Math. Monthly</journal>
  <year>2008</year>
  <volume>115</volume>
  <number>7</number>
  <pages>615-622</pages>
  <mrnumber></mrnumber>
</article></entry>

<entry id="Higman74"><book>
  <author>
    <name><first>Graham</first><last>Higman</last></name>
  </author>
  <title>Finitely Presented Infinite Simple Groups</title>
  <publisher>Department of Pure Mathematics, Australian National University, Canberra</publisher>
  <year>1974</year>
  <series>Notes on Pure Mathematics</series>
  <isbn>0-7081-0300-6</isbn>
  <mrnumber>0376874 (51 #13049)</mrnumber>
</book></entry>

<entry id="HoltEickOBrien05"><book>
  <author>
    <name><first>Derek F.</first><last>Holt</last></name>
    <name><first>Bettina</first><last>Eick</last></name>
    <name><first>Eamonn A.</first><last>O'Brien
  </author>
  <title>Handbook of Computational Group Theory</title>
  <publisher>Chapman & Hall / CRC, Boca Raton, FL</publisher>
  <year>2005</year>
  <series>Discrete Mathematics and its Applications (Boca Raton)</series>
  <isbn>1-58488-372-3</isbn>
  <mrnumber>2129747 (2006f:20001)</mrnumber>
  <other type="pages">xvi+514</other>
</book></entry>

<entry id="Keller99"><article>
  <author>
    <name><first>Timothy P.</first><last>Keller</last></name>
  </author>
  <title>Finite Cycles of Certain Periodically Linear Permutations</title>
  <journal>Missouri J. Math. Sci.</journal>
  <year>1999</year>
  <volume>11</volume>
  <number>3</number>
  <pages>152-157</pages>
  <mrnumber>1717767</mrnumber>
</article></entry>

<entry id="Kohl05"><phdthesis>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title><C>Restklassenweise affine Gruppen</C></title>
  <school>Universität Stuttgart</school>
  <year>2005</year>
  <type>Dissertation</type>
  <note><URL>https://d-nb.info/977164071</URL></note>
</phdthesis></entry>

<entry id="Kohl07a"><article>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    Wildness of Iteration of Certain Residue-Class-Wise Affine Mappings
  </title>
  <journal>Adv. in Appl. Math.</journal>
  <year>2007</year>
  <volume>39</volume>
  <number>3</number>
  <pages>322-328</pages>
  <mrnumber>2352043</mrnumber>
  <note>DOI: 10.1016/j.aam.2006.08.003</note>
</article></entry>

<entry id="Kohl07b"><misc>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    Graph Theoretical Criteria for the Wildness of Residue-Class-Wise Affine Permutations
  </title>
  <year>2007</year>
  <other type="note">
    Preprint (short note),
    <URL>https://www.gap-system.org/DevelopersPages/StefanKohl/preprints/graphcrit.pdf</URL>
  </other>
</misc></entry>

<entry id="Kohl07c"><misc>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    A Reformulation of the 3n+1 Conjecture in Terms of a Mapping
    from the Free Monoid of Rank 2 to the Positive Integers
  </title>
  <year>2007</year>
  <other type="note">
    Preprint (short note),
    <URL>https://www.gap-system.org/DevelopersPages/StefanKohl/preprints/3n+1tree.pdf</URL>
  </other>
</misc></entry>

<entry id="Kohl08a"><article>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    On Conjugates of Collatz-Type Mappings
  </title>
  <journal>Int. J. Number Theory</journal>
  <year>2008</year>
  <volume>4</volume>
  <number>1</number>
  <pages>117-120</pages>
  <mrnumber>2387919</mrnumber>
  <note>DOI: 10.1142/S1793042108001237</note>
</article></entry>

<entry id="Kohl08b"><article>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    Algorithms for a Class of Infinite Permutation Groups
  </title>
  <journal>J. Symb. Comput.</journal>
  <year>2008</year>
  <volume>43</volume>
  <number>8</number>
  <pages>545-581</pages>
  <mrnumber>2415857</mrnumber>
  <note>DOI: 10.1016/j.jsc.2007.12.001</note>
</article></entry>

<entry id="Kohl09"><article>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    A Simple Group Generated by Involutions Interchanging Residue Classes
    of the Integers
  </title>
  <journal>Math. Z.</journal>
  <year>2010</year>
  <volume>264</volume>
  <number>4</number>
  <pages>927-938</pages>
  <mrnumber>2593301</mrnumber>
  <note>DOI: 10.1007/s00209-009-0497-8</note>
</article></entry>

<entry id="Kohl13"><article>
  <author>
    <name><first>Stefan</first><last>Kohl</last></name>
  </author>
  <title>
    Simple Groups Generated by Involutions Interchanging
    Residue Classes Modulo Lattices in <M>\mathbb{Z}^d</M>
  </title>
  <journal>J. Group Theory</journal>
  <year>2013</year>
  <volume>16</volume>
  <number>1</number>
  <pages>81-86</pages>
  <note>DOI: 10.1515/jgt-2012-0031</note>
</article></entry>

<entry id="Lagarias06"><misc>
  <author>
    <name><first>Jeffrey C.</first><last>Lagarias</last></name>
  </author>
  <title>The 3x+1 Problem: An Annotated Bibliography</title>
  <year>2003+</year>
  <note>
    <URL>https://arxiv.org/abs/math.NT/0309224</URL> (Part I),
    <URL>https://arxiv.org/abs/math.NT/0608208</URL> (Part II)
  </note>
</misc></entry>

<entry id="LaHarpe00"><book>
  <author>
    <name><first>Pierre</first><last>de la Harpe</last></name>
  </author>
  <title>Topics in Geometric Group Theory</title>
  <publisher>Chicago Lectures in Mathematics</publisher>
  <year>2000</year>
  <isbn>0-226-31721-8</isbn>
  <mrnumber>1786869 (2001i:20081)</mrnumber>
</book></entry>

<entry id="LyndonSchupp77"><book>
  <author>
    <name><first>Roger C.</first><last>Lyndon</last></name>
    <name><first>Paul E.</first><last>Schupp</last></name>
  </author>
  <title>Combinatorial Group Theory</title>
  <publisher>Springer-Verlag</publisher>
  <year>1977</year>
  <note>Reprinted in the Springer Classics in Mathematics Series, 2000.</note>
  <isbn>3-540-41158-5</isbn>
  <mrnumber>0577064 (58 #28182)</mrnumber>
</book></entry>

<entry id="MatthewsLeigh87"><article>
  <author>
    <name><first>K. R.</first><last>Matthews</last></name>
    <name><first>G. M.</first><last>Leigh</last></name>
  </author>
  <title>
    A Generalization of the <C>Syracuse</C> Algorithm in
    <C>GF(<M>q</M>)[<M>x</M>]</C>
  </title>
  <journal>J. Number Theory</journal>
  <year>1987</year>
  <volume>25</volume>
  <pages>274-278</pages>
  <mrnumber>0880462 (88f:11116)</mrnumber>
</article></entry>

<entry id="Mihailova58"><article>
  <author>
    <name><first>K. A.</first><last>Mihailova</last></name>
  </author>
  <title>The Occurrence Problem for Direct Products of Groups</title>
  <journal>Dokl. Acad. Nauk. SSSR</journal>
  <year>1958</year>
  <volume>119</volume>
  <pages>1103-1105</pages>
  <mrnumber>0100018 (20 #6454)</mrnumber>
</article></entry>

<entry id="Polycyclic"><manual>
  <author>
    <name><first>Bettina</first><last>Eick</last></name>
    <name><first>Max</first><last>Horn</last></name>
    <name><first>Werner</first><last>Nickel</last></name>
  </author>
  <title>
    <C>Polycyclic -- Computation with polycyclic groups (Version 2.11)</C>
  </title>
  <year>2013</year>
  <other type="note">
    GAP package, <URL>https://www.gap-system.org/Packages/polycyclic.html</URL>
  </other>
</manual></entry>

<entry id="Utils"><manual>
  <author>
    <name><first>Sebastian</first><last>Gutsche</last></name>
    <name><first>Stefan</first><last>Kohl</last></name>
    <name><first>Christopher</first><last>Wensley</last></name>
  </author>
  <title>
    <C>Utils - Utility functions in GAP (Version 0.38)</C>
  </title>
  <year>2016</year>
  <other type="note">
    GAP package, <URL>https://www.gap-system.org/Packages/utils.html</URL>
  </other>
</manual></entry>

<entry id="Venturini92"><article>
  <author>
    <name><first>G.</first><last>Venturini</last></name>
  </author>
  <title>
    Iterates of Number-Theoretic Functions with Periodic Rational
    Coefficients (Generalization of the <M>3x+1</M> Problem)
  </title>
  <journal>Stud. Appl. Math</journal>
  <year>1992</year>
  <volume>86</volume>
  <pages>185-218</pages>
  <mrnumber>1150010 (93b:11102)</mrnumber>
</article></entry>

<entry id="Wirsching98"><book>
  <author>
    <name><first>Günther J.</first><last>Wirsching</last></name>
  </author>
  <title>The Dynamical System Generated by the <M>3n+1</M> Function</title>
  <publisher>Springer-Verlag</publisher>
  <year>1998</year>
  <number>1681</number>
  <series>Lecture Notes in Mathematics</series>
  <isbn>3-540-63970-5</isbn>
  <mrnumber>1612686 (99g:11027)</mrnumber>
</book></entry>

</file>

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