On K-\(\mathbb P\)-subnormal subgroups of finite groups. (English. Russian original) Zbl 1330.20033

Vasil’ev, A. F.; Vasil’eva, T. I.; Tyutyanov, V. N.

Math. Notes 95, No. 4, 471-480 (2014); translation from Mat. Zametki 95, No. 4, 517-528 (2014).

Summary: A subgroup \(H\) of a group \(G\) is said to be K-\(\mathbb P\)-subnormal in \(G\) if \(H\) can be joined to the group by a chain of subgroups each of which is either normal in the next subgroup or of prime index in it. Properties of K-\(\mathbb P\)-subnormal subgroups are obtained. A class of finite groups whose Sylow \(p\)-subgroups are K-\(\mathbb P\)-subnormal in \(G\) for every \(p\) in a given set of primes is studied. Some products of K-\(\mathbb P\)-subnormal subgroups are investigated.

MSC:

20D35	Subnormal subgroups of abstract finite groups
20D20	Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D40	Products of subgroups of abstract finite groups
20D30	Series and lattices of subgroups

Keywords:

finite groups; Sylow subgroups; K-\(\mathbb P\)-subnormal subgroups; normal subgroups; subgroups of prime index; supersolvable groups; formations of groups; chains of subgroups; products of subgroups

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