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

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.


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
Full Text: DOI


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