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A Simplicity Criterion for Finite Groups

โœ Scribed by Huiwen Deng; Wujie Shi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
193 KB
Volume
191
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

In this paper, we investigate the relation between the number of primes and that of ลฝ . composite numbers in G and obtain a criterion for the simplicity of finite e groups. แฎŠ 1997 Academic Press 1. INTRODUCTION Throughout this paper, all groups are finite and all simple groups are nonabelian.

Given a group G, we denote the set of all prime divisors of order G by ลฝ . ลฝ . ลฝ . G and the set of all element orders of G by G . Clearly, G is the e ลฝ .

< < set consisting of primes that lies in G . Usually X denotes the number e of elements of a set X. For convenience, we define G s the number of composite numbers in G ,

ลฝ .

ลฝ .

e ลฝ . ลฝ . ร„ 4 which in fact is the number of elements of G y G y 1 . All e further unexplained notation is standard and can be found, for example, in w x 4 .

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