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The structure of finite groups and the \(\theta\)-pairs of subgroups. (English) Zbl 1217.20011
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palack√Ĺ 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].

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