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).