the $n$-ary adding machine and solvable groups
نویسندگان
چکیده
we describe under various conditions abelian subgroups of the automorphism group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$, which are normalized by the $n$-ary adding machine $tau =(e, dots, e,tau )sigma _{tau }$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1, dots, n-1right) $. as an application, for $n=p$ a prime number, and for $n=4$, we prove that every soluble subgroup of $mathrm{aut}(t_{n})$, containing $tau $ is an extension of a torsion-free metabelian group by a finite group.
منابع مشابه
THE n-ARY ADDING MACHINE AND SOLVABLE GROUPS
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 met...
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عنوان ژورنال:
international journal of group theoryجلد ۲، شماره ۴، صفحات ۴۳-۸۸
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