Gustavo A. Fernández-Alcober
GGS-groups: order of congruence quotients and Hausdorff dimension.
Fri, 08/12/2011 - 15:01 — SomNambulAuthors: Gustavo A. Fernández-Alcober, Amaia Zugadi-Reizabal
Subjects: Group Theory
AbstractIf G is a GGS-group defined over a p-adic tree, where p is an odd prime, we
calculate the order of the congruence quotients $G_n=G/\Stab_G(n)$ for every n.
If G is defined by the vector $e=(e_1,...,e_{p-1})\in\F_p^{p-1}$, the
determination of the order of $G_n$ is split into three cases, according as e
is non-symmetric, non-constant symmetric, or constant. The formulas that we
obtain only depend on p, n, and the rank of the circulant matrix whose first
row is e.A focal subgroup theorem for outer commutator words.
Fri, 08/12/2011 - 15:01 — SomNambulAuthors: Criatina Acciarri, Gustavo A. Fernández-Alcober, Pavel Shumyatsky
Subjects: Group Theory
AbstractLet $G$ be a finite group of order $p^am$, where $p$ is a prime and $m$ is
not divisible by $p$, and let $P$ be a Sylow $p$-subgroup of $G$. If $w$ is an
outer commutator word, we prove that $P\cap w(G)$ is generated by the
intersection of $P$ with the set of $m$th powers of all values of $w$ in $G$
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