On the Magnus Function
Roger C. Alperin
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1 Introduction
There are uncountably many integer functions M : Z ¡! Z having the
properties
M(0) = 0;M(M(x)) = x;M(x) = M(M(x ¡ 1) ¡ 1) ¡ 1:
Using this B. Neumann [cf. M2] showed the existence of uncountably many
maximal non-parabolic subgroups of the modular group PSL2(Z).
J. Kock. (2008)cite arxiv:0807.2874
Comment: 50 pages, LaTeX; uses Paul Taylor's diagrams and Peter Kabal's
texdraw; does not compile with pdlaftex. v2: expository improvements
throughout. v3: a few typos corrected and references updated. To appear in
IMRN.