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1982•Mathematics of the USSR-SbornikRequires access

SIMPLE GROUPS WITH LARGE SYLOW SUBGROUPS

A. V. Romanovskii

Open publisher page 2 citations

Abstract

A. I. Kostrikin posed the problem of the structure of a simple group having a Sylow -subgroup for which , and whenever . It has been established by the author that , and are the only simple groups of this kind. Earlier Brauer and Reynolds have found the solution to the problem of Artin which is the partial case of Kostrikin's problem when . One of the results used in the proof of the main theorem of the author leads to the following group-theoretical characterization of : a simple group is isomorphic to , , if and only if contains a -subgroup of odd order distinct from its own normalizer in , and such that . Bibliography: 28 titles.

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What this paper is about

A. I. Kostrikin posed the problem of the structure of a simple group having a Sylow -subgroup for which , and whenever . It has been established by the author that , and are the only simple groups of this kind. Earlier Brauer and Reynolds have found the solution to the problem of Artin which is the partial case of Kostrikin's problem when . One of the results used in the proof of the main theorem of the author leads to the following group-theoretical characterization of : a simple group is isomorphic to , , if and only if contains a -subgroup of odd order distinct from its own normalizer in , and such that . Bibliography: 28 titles.

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Available abstract

A. I. Kostrikin posed the problem of the structure of a simple group having a Sylow -subgroup for which , and whenever . It has been established by the author that , and are the only simple groups of this kind. Earlier Brauer and Reynolds have found the solution to the problem of Artin which is the partial case of Kostrikin's problem when . One of the results used in the proof of the main theorem of the author leads to the following group-theoretical characterization of : a simple group is isomorphic to , , if and only if contains a -subgroup of odd order distinct from its own normalizer in , and such that . Bibliography: 28 titles.

Key concepts: Sylow theorems, Centralizer and normalizer, Simple group, Mathematics, Simple (philosophy), Locally finite group, Classification of finite simple groups, Group (periodic table)

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