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da Silva Rocha, Josimar, Sidki, Said. (1392). The $n$-ary adding machine and solvable groups. , 2(4), 43-88. doi: 10.22108/ijgt.2013.2871
Josimar da Silva Rocha; Said Sidki. "The $n$-ary adding machine and solvable groups". , 2, 4, 1392, 43-88. doi: 10.22108/ijgt.2013.2871
da Silva Rocha, Josimar, Sidki, Said. (1392). 'The $n$-ary adding machine and solvable groups', , 2(4), pp. 43-88. doi: 10.22108/ijgt.2013.2871
da Silva Rocha, Josimar, Sidki, Said. The $n$-ary adding machine and solvable groups. , 1392; 2(4): 43-88. doi: 10.22108/ijgt.2013.2871

The $n$-ary adding machine and solvable groups

International Journal of Group Theory
مقاله 7، دوره 2، شماره 4، اسفند 2013، صفحه 43-88    اصل مقاله (693.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2871
نویسندگان
Josimar da Silva Rocha1؛ Said Sidki* 2
1Instituto Federal de Educacao
2Universidade De Brasilia
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-1\right) $‎. ‎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.
کلیدواژه‌ها
Adding machine؛ Tree automorphisms؛ Automata؛ solvable groups
مراجع
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