\begin{thebibliography}{Koh07b}

\bibitem[And00]{Andaloro00}
P.~Andaloro.
\newblock On total stopping times under $3x+1$ iteration.
\newblock {\em Fibonacci Quarterly}, 38:73--78, 2000.

\bibitem[Bar07]{FR}
L.~Bartholdi.
\newblock {\em {FR -- Computations with functionally recursive groups. Version
  0.714285}}, 2007.
\newblock GAP package, \href {http://mad.epfl.ch/~laurent/FR/}
  {\texttt{http://mad.epfl.ch/}\discretionary
  {}{}{}\texttt{\texttt{\symbol{126}}laurent/}\discretionary
  {}{}{}\texttt{FR/}}.

\bibitem[dlH00]{LaHarpe00}
P.~de~la Harpe.
\newblock {\em Topics in Geometric Group Theory}.
\newblock Chicago Lectures in Mathematics, 2000.

\bibitem[EN06]{Polycyclic}
B.~Eick and W.~Nickel.
\newblock {\em {Polycyclic -- Computation with polycyclic groups; Version
  2.1}}, 2006.
\newblock GAP package, \href
  {http://www.gap-system.org/Packages/polycyclic.html}
  {\texttt{http://www.gap-system.org/}\discretionary
  {}{}{}\texttt{Packages/}\discretionary {}{}{}\texttt{polycyclic.html}}.

\bibitem[Gri80]{Grigorchuk80}
R.~I. Grigorchuk.
\newblock Burnside's problem on periodic groups.
\newblock {\em Functional Anal. Appl.}, 14:41--43, 1980.

\bibitem[GT02]{GluckTaylor02}
D.~Gluck and B.~D. Taylor.
\newblock A new statistic for the $3x+1$ problem.
\newblock {\em Proc. Amer. Math. Soc.}, 130(5):1293--1301, 2002.

\bibitem[HEO05]{HoltEickOBrien05}
D.~F. Holt, B.~Eick, and E.~A. O'Brien.
\newblock {\em Handbook of Computational Group Theory}.
\newblock Discrete Mathematics and its Applications (Boca Raton). Chapman \&
  Hall / CRC, Boca Raton, FL, 2005.

\bibitem[Kel99]{Keller99}
T.~P. Keller.
\newblock Finite cycles of certain periodically linear permutations.
\newblock {\em Missouri J. Math. Sci.}, 11(3):152--157, 1999.

\bibitem[Koh05]{Kohl05}
S.~Kohl.
\newblock {\em {Restklassenweise affine Gruppen}}.
\newblock Dissertation, Universit{\"a}t Stuttgart, 2005.
\newblock \href {http://deposit.ddb.de/cgi-bin/dokserv?idn=977164071}
  {\texttt{http://deposit.ddb.de/}\discretionary
  {}{}{}\texttt{cgi-bin/}\discretionary {}{}{}\texttt{dokserv?idn=977164071}}.

\bibitem[Koh06a]{Kohl06b}
S.~Kohl.
\newblock A simple group generated by involutions interchanging residue classes
  of the integers, 2006.
\newblock \href
  {http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/simplegp.pdf}
  {\texttt{http://www.cip.mathematik.uni-stuttgart.de/}\discretionary
  {}{}{}\texttt{\texttt{\symbol{126}}kohlsn/}\discretionary
  {}{}{}\texttt{preprints/}\discretionary {}{}{}\texttt{simplegp.pdf}}.

\bibitem[Koh06b]{Kohl06a}
S.~Kohl.
\newblock Wildness of iteration of certain residue-class-wise affine mappings.
\newblock {\em Adv. in Appl. Math.}, 2006.
\newblock doi:10.1016/j.aam.2006.08.003.

\bibitem[Koh07a]{Kohl07b}
S.~Kohl.
\newblock Graph theoretical criteria for the wildness of residue-class-wise
  affine permutations, 2007.
\newblock \href
  {http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/graphcrit.pdf}
  {\texttt{http://www.cip.mathematik.uni-stuttgart.de/}\discretionary
  {}{}{}\texttt{\texttt{\symbol{126}}kohlsn/}\discretionary
  {}{}{}\texttt{preprints/}\discretionary {}{}{}\texttt{graphcrit.pdf}}.

\bibitem[Koh07b]{Kohl07a}
S.~Kohl.
\newblock A new class of groups which are accessible to computational methods,
  2007.
\newblock \href
  {http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/preprints/compute.pdf}
  {\texttt{http://www.cip.mathematik.uni-stuttgart.de/}\discretionary
  {}{}{}\texttt{\texttt{\symbol{126}}kohlsn/}\discretionary
  {}{}{}\texttt{preprints/}\discretionary {}{}{}\texttt{compute.pdf}}.

\bibitem[Lag06]{Lagarias06}
J.~C. Lagarias.
\newblock 3x+1 problem annotated bibliography, 2006.
\newblock \href {http://arxiv.org/abs/math.NT/0309224}
  {\texttt{http://arxiv.org/}\discretionary {}{}{}\texttt{abs/}\discretionary
  {}{}{}\texttt{math.NT/}\discretionary {}{}{}\texttt{0309224}}.

\bibitem[LN07]{GAPDoc}
F.~L{\"u}beck and M.~Neunh{\"o}ffer.
\newblock {\em {GAPDoc (Version 1.0)}}.
\newblock RWTH Aachen, 2007.
\newblock GAP package, \href {http://www.gap-system.org/Packages/gapdoc.html}
  {\texttt{http://www.gap-system.org/}\discretionary
  {}{}{}\texttt{Packages/}\discretionary {}{}{}\texttt{gapdoc.html}}.

\bibitem[Mih58]{Mihailova58}
K.~A. Mihailova.
\newblock The occurence problem for direct products of groups.
\newblock {\em Dokl. Acad. Nauk. SSSR}, 119:1103--1105, 1958.

\bibitem[ML87]{MatthewsLeigh87}
K.~R. Matthews and G.~M. Leigh.
\newblock A generalization of the {Syracuse} algorithm in {GF($q$)[$x$]}.
\newblock {\em J. Number Theory}, 25:274--278, 1987.

\bibitem[Soi02]{GRAPE}
L.~Soicher.
\newblock {\em {GRAPE -- GRaph Algorithms using PErmutation groups (Version
  4.1)}}.
\newblock Queen Mary, University of London, 2002.
\newblock GAP package, \href {http://www.gap-system.org/Packages/grape.html}
  {\texttt{http://www.gap-system.org/}\discretionary
  {}{}{}\texttt{Packages/}\discretionary {}{}{}\texttt{grape.html}}.

\end{thebibliography}
