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- Title
OVERGROUPS OF WEAK SECOND MAXIMAL SUBGROUPS.
- Authors
MENG, HANGYANG; GUO, XIUYUN
- Abstract
A subgroup $H$ is called a weak second maximal subgroup of $G$ if $H$ is a maximal subgroup of a maximal subgroup of $G$. Let $m(G,H)$ denote the number of maximal subgroups of $G$ containing $H$. We prove that $m(G,H)-1$ divides the index of some maximal subgroup of $G$ when $H$ is a weak second maximal subgroup of $G$. This partially answers a question of Flavell ['Overgroups of second maximal subgroups', Arch. Math. 64 (4) (1995), 277–282] and extends a result of Pálfy and Pudlák ['Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups', Algebra Universalis 11 (1) (1980), 22–27].
- Subjects
MAXIMAL subgroups; FINITE groups; MODULES (Algebra); HOMOMORPHISMS; VECTOR spaces
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p83
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000904