CENTRALIZERS OF p-SUBGROUPS IN SIMPLE LOCALLY FINITE GROUPS
نویسندگان
چکیده
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...
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A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
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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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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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a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq z(g)$. in this paper, we give a complete classification of finite $mathcal{cac}$-$p$-groups.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2019
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708951900003x