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# On Total Stopping Times under 3x+1 Iteration

Fibonacci Quarterly
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Meenaxi
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Dugald
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Rögnvaldur G.
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Peter M.
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# Notes on Infinite Permutation Groups

Springer-Verlag
1998
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John D.
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# Permutation Groups

Springer-Verlag
1996
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# Variants of the 3n+1 Problem and Multiplicative Semigroups

Proc. Robert Brooks Memorial Conference
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Contemp. Math.
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Laurent
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# FR -- Computations with functionally recursive groups. Version 0.714285

2007
GAP package, http://mad.epfl.ch/~laurent/FR/
Harry
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# On the Infinitude of Primes

Amer. Math. Monthly
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# GAPDoc (Version 1.0)

RWTH Aachen
2007
GAP package, http://www.gap-system.org/Packages/gapdoc.html
David
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# A New Statistic for the 3x+1 Problem

Proc. Amer. Math. Soc.
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MR1879950 (2002k:11031)
Leonard
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# GRAPE -- GRaph Algorithms using PErmutation groups (Version 4.1)

Queen Mary, University of London
2002
GAP package, http://www.gap-system.org/Packages/grape.html
Ben
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Terence
Tao

# The Primes Contain Arbitrarily Long Arithmetic Progressions

2004

http://arxiv.org/abs/math.NT/0404188v1

Rostislav I.
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# Burnside's Problem on Periodic Groups

Functional Anal. Appl.
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Derek F.
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Eamonn A.
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# Handbook of Computational Group Theory

Chapman & Hall / CRC, Boca Raton, FL
2005
Discrete Mathematics and its Applications (Boca Raton)
1-58488-372-3
MR2129747 (2006f:20001)
xvi+514
Timothy P.
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# Finite Cycles of Certain Periodically Linear Permutations

Missouri J. Math. Sci.
1999
11
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MR1717767
Stefan
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# Restklassenweise affine Gruppen

Universität Stuttgart
2005
Dissertation

http://deposit.ddb.de/cgi-bin/dokserv?idn=977164071

Stefan
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# Wildness of Iteration of Certain Residue-Class-Wise Affine Mappings

Adv. in Appl. Math.
2006

doi:10.1016/j.aam.2006.08.003

Stefan
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# A Simple Group Generated by Involutions Interchanging Residue Classes of the Integers

2006
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/simplegp.pdf
Stefan
Kohl

# A New Class of Groups which are Accessible to Computational Methods

2007
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/compute.pdf
Stefan
Kohl

# Graph Theoretical Criteria for the Wildness of Residue-Class-Wise Affine Permutations

2007
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/graphcrit.pdf
Stefan
Kohl

# A Reformulation of the 3n+1 Conjecture in Terms of a Mapping from the Free Monoid of Rank 2 to the Positive Integers

2007
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/3n+1tree.pdf
Jeffrey C.
Lagarias

# 3x+1 Problem Annotated Bibliography

2006

http://arxiv.org/abs/math.NT/0309224

Pierre
de la Harpe

# Topics in Geometric Group Theory

Chicago Lectures in Mathematics
2000
0-226-31721-8
MR1786869 (2001i:20081)
Roger C.
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Paul E.
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# Combinatorial Group Theory

Springer-Verlag
1977

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3-540-41158-5
MR0577064 (58 #28182)
K. R.
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G. M.
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# A Generalization of the Syracuse Algorithm in GF(q)[x]

J. Number Theory
1987
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MR0880462 (88f:11116)
K. A.
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# The Occurence Problem for Direct Products of Groups

Dokl. Acad. Nauk. SSSR
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MR0100018 (20 #6454)
Bettina
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Werner
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# Polycyclic -- Computation with polycyclic groups; Version 2.1

2006
GAP package, http://www.gap-system.org/Packages/polycyclic.html
G.
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# Iterates of Number-Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x+1 Problem)

Stud. Appl. Math
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MR1150010 (93b:11102)
Günther J.
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# The Dynamical System Generated by the 3n+1 Function

Springer-Verlag
1998
1681
Lecture Notes in Mathematics
3-540-63970-5
MR1612686 (99g:11027)