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- Title
Some generalizations of Shao and Beltrán's theorem.
- Authors
Li, Minghui; Lu, Jiakuan; Zhang, Boru; Meng, Wei
- Abstract
Let G and A be finite groups of relative coprime orders and A act on G via automorphisms. In this paper, we prove that when every maximal A-invariant subgroup of G that contains the normalizer of some Sylow subgroup has prime index, then G is supersolvable; if every non-nilpotent maximal A-invariant subgroup of G has prime index or is normal in G, then G is a Sylow tower group.
- Subjects
MAXIMAL subgroups; FINITE groups; SYLOW subgroups; GENERALIZATION
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 3, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823500676