THE n-ARY ADDING MACHINE AND SOLVABLE GROUPS
نویسندگان
چکیده
We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free metabelian group by a finite group.
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