Maximal subgroups in finite and profinite groups

Maximal subgroups in finite and profinite groups
复制标题

有限群和有限群中的最大子群

DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A. Shalev
A. Shalev
中科院分区：
--
文献类型：
--
作者：
A. Borovik;L. Pyber;A. Shalev

文献摘要

被引文献

相似文献

本文证明了：如果一个有限生成的有限群G不是由任意多个随机元以正概率生成的，则每个有限群F都是G的一个开子群的商。证明涉及研究profinite群的极大子群，以及有限置换群和有限Chevalley群的技术。证明了有限群G至多有IGIc个极大可解子群，并指出这一结果在各种计数问题中是相当有用的.
We prove that if a finitely generated profinite group G is not generated with positive probability by finitely many random elements, then every finite group F is obtained as a quotient of an open subgroup of G. The proof involves the study of maximal subgroups of profinite groups, as well as techniques from finite permutation groups and finite Chevalley groups. Confirming a conjecture from Ann. of Math. 137 (1993), 203-220, we then prove that a finite group G has at most IGIc maximal soluble subgroups, and show that this result is rather useful in various enumeration problems.