Sobre a influência dos centralizadores dos automorfismos de ordem dois em grupos de ordem ímpar
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2013-07-05
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Universidade Federal de Goiás
Resumo
This document presents an approach and development of some of the results of
Shumyatsky in [14, 15, 16, 17, 18], where he worked with automorphisms of order two
in finite groups of odd order, mainly showing the influence that the structure of the
centralizer has on that of Group. Let G be a group with odd order, and ϕ an automorphism
on G, of order two, where G = [G,ϕ], and given a limitation in the order of the centralizer
of ϕ regard to G, CG(ϕ), which induces a limitation in the order of derived group G′ of
group G, and we also verified that G has a normal subgroup H that is ϕ-invariant, such
that H′ ≤ Gϕ and its index [G : H] is bounded with the initial limitation. With the same
hypothesis of the group G and with the same limitation of the order of the centralizer of
the automorphism, let V a abelian p-group such that G⟨ϕ⟩ act faithful and irreductible
on V, then there is a bounded constant k, limitated by a function depending only on the
parameter m, where m is tha limitation in the order of CG(ϕ), and elements x1, ...xk ∈ G−ϕ
such that V = ρϕx
1,...,xk(V−ϕ).
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Citação
ROJAS, Yerko Contreras. Sobre a Influência dos Centralizadores dos Automorfismos de Ordem Dois em Grupos de Ordem Ímpar. 2013. 59 f. Dissertação (Mestrado em Matemática ) - Universidade Federal de Goiás, Goiânia, 2013.