摘要
Ａｎｏｔｅｏｎｔｗｏｃｏｎｊｅｃｔｕｒｅｓｏｆｆｉｎｉｔｅｓｉｍｐｌｅｇｒｏｕｐｓ￥ＬｉｕＪｉａｎｊｕｎ；ＣｈｅｎｇＨａｉｃｈｕａｎ；ＬｉＸｉａｎｈｕａ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｗｅｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖ...
Let πs (G) and πt (G) denote the set of orders and indexes of maximal subgroups of a finite group G, respectively. Wang Dianjun and Li Xianhua put forward the following conjectures,respectively:Conjecture Ⅰ: Let M be a finite simple group and C a group, then C ≌ M if and only if πs (G) =πs (M).Conjecture Ⅱ: Let N and M be all nonabelian simple groups. If and | N | | M |, then N ≌ M or N ≌ PSL(2,11) while M ≌ M11.In this short paper, that the conjecture Ⅱ implies the conjecture Ⅰ is proved. Therefore, the proof of the conjecture Ⅰ can be reduced to consider the problem just for simple groups.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1996年第5期415-418,共4页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
有限单群
猜想
浮记
nonsolvable groups
maximal subgroups
index
