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<h3>References</h3>

<a id="biBAndaloro00" name="biBAndaloro00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1738650">And00</a>] Andaloro, P.,
On Total Stopping Times under \(3x+1\) Iteration,
Fibonacci Quarterly,
38
(2000),
73-78.


<a id="biBFR" name="biBFR"></a>

[Bar15] Bartholdi, L.,

 FR -- Computations with functionally recursive groups. Version 2.2.1
 
(2015) 
(
 GAP package, <a href="https://www.gap-system.org/Packages/fr.html">https://www.gap-system.org/Packages/fr.html</a>
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<a id="biBLaHarpe00" name="biBLaHarpe00"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1786869">dlH00</a>] de la Harpe, P.,
Topics in Geometric Group Theory,
Chicago Lectures in Mathematics
(2000).


<a id="biBPolycyclic" name="biBPolycyclic"></a>

[EHN13] Eick, B., Horn, M. and Nickel, W.,

 Polycyclic -- Computation with polycyclic groups (Version 2.11)
 
(2013) 
(
 GAP package, <a href="https://www.gap-system.org/Packages/polycyclic.html">https://www.gap-system.org/Packages/polycyclic.html</a>
 ).


<a id="biBUtils" name="biBUtils"></a>

[GKW16] Gutsche, S., Kohl, S. and Wensley, C.,

 Utils - Utility functions in GAP (Version 0.38)
 
(2016) 
(
 GAP package, <a href="https://www.gap-system.org/Packages/utils.html">https://www.gap-system.org/Packages/utils.html</a>
 ).


<a id="biBGrigorchuk80" name="biBGrigorchuk80"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0565099">Gri80</a>] Grigorchuk, R. I.,
Burnside's Problem on Periodic Groups,
Functional Anal. Appl.,
14
(1980),
41-43.


<a id="biBGluckTaylor02" name="biBGluckTaylor02"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1879950">GT02</a>] Gluck, D. and Taylor, B. D.,
A New Statistic for the \(3x+1\) Problem,
Proc. Amer. Math. Soc.,
130 (5)
(2002),
1293-1301.


<a id="biBHoltEickOBrien05" name="biBHoltEickOBrien05"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2129747">HEO05</a>] Holt, D. F., Eick, B. and O'Brien, E. A.,
Handbook of Computational Group Theory,
Chapman & Hall / CRC, Boca Raton, FL,
Discrete Mathematics and its Applications (Boca Raton)
(2005),
xvi+514 pages.


<a id="biBHigman74" name="biBHigman74"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0376874">Hig74</a>] Higman, G.,
Finitely Presented Infinite Simple Groups,
Department of Pure Mathematics, Australian National University, Canberra,
Notes on Pure Mathematics
(1974).


<a id="biBKeller99" name="biBKeller99"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1717767">Kel99</a>] Keller, T. P.,
Finite Cycles of Certain Periodically Linear Permutations,
Missouri J. Math. Sci.,
11 (3)
(1999),
152-157.


<a id="biBKohl05" name="biBKohl05"></a>

[Koh05] Kohl, S.,
Restklassenweise affine Gruppen,
Dissertation,
Universität Stuttgart
(2005) 
(<a href="https://d-nb.info/977164071">https://d-nb.info/977164071</a>).


<a id="biBKohl07b" name="biBKohl07b"></a>

[Koh07a] Kohl, S.,

 Graph Theoretical Criteria for the Wildness of Residue-Class-Wise Affine Permutations
 
(2007) 
(
 Preprint (short note),
 <a href="https://www.gap-system.org/DevelopersPages/StefanKohl/preprints/graphcrit.pdf">https://www.gap-system.org/DevelopersPages/StefanKohl/preprints/graphcrit.pdf</a>
 ).


<a id="biBKohl07a" name="biBKohl07a"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2352043">Koh07b</a>] Kohl, S.,

 Wildness of Iteration of Certain Residue-Class-Wise Affine Mappings
 ,
Adv. in Appl. Math.,
39 (3)
(2007),
322-328 
(DOI: 10.1016/j.aam.2006.08.003).


<a id="biBKohl08b" name="biBKohl08b"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2415857">Koh08</a>] Kohl, S.,

 Algorithms for a Class of Infinite Permutation Groups
 ,
J. Symb. Comput.,
43 (8)
(2008),
545-581 
(DOI: 10.1016/j.jsc.2007.12.001).


<a id="biBKohl09" name="biBKohl09"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2593301">Koh10</a>] Kohl, S.,

 A Simple Group Generated by Involutions Interchanging Residue Classes
 of the Integers
 ,
Math. Z.,
264 (4)
(2010),
927-938 
(DOI: 10.1007/s00209-009-0497-8).


<a id="biBKohl13" name="biBKohl13"></a>

[Koh13] Kohl, S.,

 Simple Groups Generated by Involutions Interchanging
 Residue Classes Modulo Lattices in \(\mathbb{Z}^d\)
 ,
J. Group Theory,
16 (1)
(2013),
81-86 
(DOI: 10.1515/jgt-2012-0031).


<a id="biBLagarias06" name="biBLagarias06"></a>

[Lag03] Lagarias, J. C.,
The 3x+1 Problem: An Annotated Bibliography
(2003+) 
(
 <a href="https://arxiv.org/abs/math.NT/0309224">https://arxiv.org/abs/math.NT/0309224</a> (Part I),
 <a href="https://arxiv.org/abs/math.NT/0608208">https://arxiv.org/abs/math.NT/0608208</a> (Part II)
 ).


<a id="biBGAPDoc" name="biBGAPDoc"></a>

[LN12] Lübeck, F. and Neunhöffer, M.,
GAPDoc (Version 1.5.1),
RWTH Aachen
(2012) 
(
 GAP package, <a href="https://www.gap-system.org/Packages/gapdoc.html">https://www.gap-system.org/Packages/gapdoc.html</a>
 ).


<a id="biBMatthewsLeigh87" name="biBMatthewsLeigh87"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0880462">ML87</a>] Matthews, K. R. and Leigh, G. M.,

 A Generalization of the Syracuse Algorithm in
 GF(\(q\))[\(x\)]
 ,
J. Number Theory,
25
(1987),
274-278.


<a id="biBGRAPE" name="biBGRAPE"></a>

[Soi16] Soicher, L.,
GRAPE -- GRaph Algorithms using PErmutation groups (Version 4.7),
Queen Mary, University of London
(2016) 
(
 GAP package, <a href="https://www.gap-system.org/Packages/grape.html">https://www.gap-system.org/Packages/grape.html</a>
 ).


 

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