منابع مشابه
centralizers in simple locally finite groups
this is a survey article on centralizers of finite subgroups in locally finite, simple groups or lfs-groups as we will call them. we mention some of the open problems about centralizers of subgroups in lfs-groups and applications of the known information about the centralizers of subgroups to the structure of the locally finite group. we also prove the following: let $g$ be...
متن کاملCentralizers in Locally Finite Groups
The topic of the present paper is the following question. Let G be a locally finite group admitting an automorphism φ of finite order such that the centralizer CG(φ) satisfies certain finiteness conditions. What impact does this have on the structure of the group G? Equivalently, one can ask the same question when φ is an element of G. Sometimes the impact is quite strong and the paper is a sur...
متن کاملRepresentations of Locally Finite Groups
The purpose of this paper is to give a brief general account of the completely reducible finite-dimensional representations of a locally finite group G over a given algebraically closed field K. Theorem 1 shows that all such representations of G can be brought down to the algebraic closure F in K of the prime field of K. This reduces all further considerations in this account to countable group...
متن کاملOn weakly $mathfrak{F}_{s}$-quasinormal subgroups of finite groups
Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...
متن کاملInert subgroups of uncountable locally finite groups
Let G be an uncountable universal locally finite group. We study subgroups H < G such that for every g ∈ G, |H : H ∩H| < |H|.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1987
ISSN: 0035-7596
DOI: 10.1216/rmj-1987-17-1-59