The n-ary Adding Machine and Soluble Groups

Details The n-ary Adding Machine and Soluble Groups The n-ary Adding Machine and Soluble Groups

2011-08-17

arxiv.org/abs/1108.3373v3

Mathematics

Group Theory

52 pages

Scientific paper

We describe under a variety of conditions abelian subgroups of the automorphism group A of the regular n-ary tree T which are normalized by the n-ary adding machine t=(e,...,e,t)s where s is the n-cycle (0,1,...,n-1). As an application, for n a prime number, and for n = 4 we prove that every finitely generated soluble subgroup of A containing t is an extension of a torsion-free metabelian group by a finite group.

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