The structure of finite groups and the \(\theta\)-pairs of subgroups. (English) Zbl 1217.20011

Li, Xianhua; Nan, Ailing

Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 155-158 (2010).

Summary: Using the concept \(\theta\)-pairs of proper subgroups of a finite group we obtain criteria for supersolvability and nilpotency. This generalizes our previous results.
For the entire collection see [Zbl 1201.08001].

MSC:

20D40	Products of subgroups of abstract finite groups
20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D15	Finite nilpotent groups, \(p\)-groups
20E28	Maximal subgroups

Keywords:

finite groups; supersolvability; \(\theta\)-pairs; maximal subgroups; nilpotency