A finiteness condition on centralizers in locally finite groups
نویسندگان
چکیده
منابع مشابه
Centralizers 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...
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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...
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Our concern in this paper is to obtain information about the structure of centralizers of elements of locally finite simple groups, in the light of the classification of finite simple groups (CFSG). This classification, in the form that the number of sporadic simple groups is finite, is frequently used, as seems inevitable if real progress with locally finite simple groups is to be made. Centra...
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For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
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It has been known for a long time that the structure of a finite simple group is intimately connected with the structure of the centralizers of its involutions. An old result of Brauer and Fowler asserts, in fact, that there are at most a finite number of simple groups in which the centralizer of an involution has a given structure. A more specific, pioneering result of Brauer established that ...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2016
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-016-0939-4