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.

Made available in DSpace on 2014-07-29T16:02:19Z (GMT). No. of bitstreams: 1 Dissertacao Marcio Lima.pdf: 1529346 bytes, checksum: c6a80a13d55b40203c44877c4cdeb1f4 (MD5) Previous issue date: 2011-06-27 / A be an elementary abelian group of order q2, where q a prime number. In this paper we will study the influence of centering on the structure of automorphism groups profinitos in this sense if A acting as a coprime group of automorphisms on a group profinito G and CG(a) is periodic for each a 2 A#, then we will show that G is locally finite. It will be demonstrated also the case where A acts as a group of automorphisms of a group pro-p of G / Sejam A um grupo abeliano elementar de ordem q2, onde q um número primo. Neste trabalho estudamos a influência dos centralizadores de automorfismos na estrutura dos grupos profinitos, neste sentido se A age como um grupo de automorfismos coprimos sobre um grupo profinito G e que CG(a) é periódico para cada a 2 A#, então mostraremos que G é localmente finito. Será demonstrado também o caso onde A age como um grupo de automorfismos sobre um grupo pro-p de G.