Sylow Theory, Formations and Fitting Classes in Locally Finite Groups

Sylow Theory, Formations and Fitting Classes in Locally Finite Groups

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This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. It also contains details of Sunkov's and Belyaev'ss results on locally finite groups with min-p for all primes p. This is the first time many of these topics have appeared in book form. The body of work here is fairly complete. Contents:Basic Concepts:Group Theoretical Classes and Closure OperationsRadicals and ResidualsLocal SystemsThe Minimum Condition and Cernikov GroupsSylow Theory in Locally Finite Groups:The Asar-Hartley Theorem for a General Set of PrimesGroups with min-pGood Sylow SubgroupsGroups Satisfying min-p for All Primes p:Sylow Theory in Groups with min-p for All Primes pThe 2-Radicable part of a group with min-p for All pThe Structure of Groups with min-p for all primes pGroups with Conjugate Sylow Subgroups:Upper I€-Separable GroupsGroups with the Minimum Condition on CentralizersCompletely Sylow Integrated GroupsMetabelian Groups with min-nSylow Bases in Locally Finite Groups:Sylow Bases in Groups with min-p for All pCo-Hopfian GroupsFormation Theory in Locally Finite Groups:Locally Defined FormationsFitting Classes in Locally Finite Groups:Elementary Properties of Fitting ClassesInjectors in Groups with min-p for All Primes p Readership: Mathematicians. keywords:Locally Finite Group;Sylow Subgroup;Conjugacy;Local Conjugacy;Formation;Fitting Class;Sylow Basis... possibility that P and Q are Sylow subgroups relative to different sets of primes. The main result here is the following: 2.6.5. Theorem. Suppose that G is an upper n-separable group for w = 7Ti, ... , 7rn and suppose that Pi is a good Sylow iTianbsp;...

Title:Sylow Theory, Formations and Fitting Classes in Locally Finite Groups
Author: Martyn R Dixon
Publisher: - 1994-12-09

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