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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, 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