Inert Subgroups And Centralizers Of Involutions In Locally Finite Simple Groups

Description

abstract
INERT SUBGROUPS AND CENTRALIZERS OF
INVOLUTIONS IN LOCALLY FINITE SIMPLE
GROUPS
&uml / Ozyurt, Erdal
Ph. D., Department of Mathematics
Supervisor: Prof. Dr. Mahmut Kuzucuo&amp / #728 / glu
September 2003, 68 pages
A subgroup H of a group G is called inert if [H : H Hg] is finite for all
g 2 G. A group is called totally inert if every subgroup is inert. Among the
basic properties of inert subgroups, we prove the following. Let M be a maximal
subgroup of a locally finite group G. If M is inert and abelian, then G is soluble
with derived length at most 3. In particular, the given properties impose a strong
restriction on the derived length of G.
We also prove that, if the centralizer of every involution is inert in an infinite
locally finite simple group G, then every finite set of elements of G can not be
contained in a finite simple group. In a special case, this generalizes a Theorem
of Belyaev&amp / #8211 / Kuzucuo&amp / #728 / glu&amp / #8211 / Se&cedil / ckin, which proves that there exists no infinite locally
finite totally inert simple group.

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1. http://etd.lib.metu.edu.tr/upload/1141546/index.pdf

Tags

QA Algebra 150-272.5

Additional Fields

Identifer	oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/1141546/index.pdf
Date	01 September 2003
Creators	Ozyurt, Erdal
Contributors	Kuzucuoglu, Mahmut
Publisher	METU
Source Sets	Middle East Technical Univ.
Language	English
Detected Language	English
Type	Ph.D. Thesis
Format	text/pdf
Rights	To liberate the content for public access