A characterization of the finite simple groups

JOURNAL OF ALGEBRA

卷:245

Article

Li, XH

关键词: finite simple group;    maximal subgroup;    index;   

DOI  :  10.1006/jabr.2001.8941

来源: Elsevier

【 摘 要 】

In this paper, we obtain a quantitative characterization of all finite simple groups. Let pi (1) (G) denote the set of indices of maximal subgroups of group G and let P(G) be the smallest number in pi (1)(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 pi (1) (N) subset of or equal to pi (1)(G), then (1) N congruent to G or (2) G = M-11 and N congruent to PSL(2, 11) or G = S-o (2) and N congruent to U-3(3). THEOREM 3. Let N be a finite simple and let G be a finite group. If \G \ = \N \ and pi (1)(G)= pi (1)(N), then G congruent to N. (C) 2001 Academic Press.

【 授权许可】

Free