Vol. 29, No. 2, 1969

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ISSN: 0030-8730
On finite groups with independent cyclic Sylow subgroups

Marcel Herzog

Vol. 29 (1969), No. 2, 285–293
Abstract

The purpose of this paper is to classify all perfect groups with cyclic Sylow p-subgroups which satisfy the condition

(TI) two different Sylow p-subgroups of G contain only the unit element in common and such that

o(G) < o(P )3

where P is a Sylow p-subgroup of G.

The main result of this paper is the following

Theorem 1. Let G be a perfect finite group with a cyclic Sylow p-subgroup P of order pa and assume that the Sylow p-subgroups of G satisfy the (TI) condition. Assume, furthermore, that

o(G ) < p3a.

Then one of the following statements holds.

(I) a = 1, GPSL(2,p), where p > 3 is a prime.

(II) a = 1, GPSL(2,p 1), where p = 2m + 1 > 5 is a Fermat prime.

(III) a = 1, GSL(2,p), where p > 3 is a prime.

(IV) a = 2, p = 3, GPSL(2,8).

Mathematical Subject Classification
Primary: 20.43
Milestones
Received: 10 May 1968
Published: 1 May 1969
Authors
Marcel Herzog