✦ LIBER ✦

A Characterization of the Finite Simple Groups

✍ Scribed by Li Xianhua

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 226 KB
Volume: 245
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8941

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✦ Synopsis

In this paper, we obtain a quantitative characterization of all finite simple groups. Let π t G denote the set of indices of maximal subgroups of group G and let P G be the smallest number in π t G . We have the following theorems.

Theorem 2. Let N and G be finite simple groups. If N divides G , P N = P G , and π t N ⊆ π t G , then

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