## 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.

### 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
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### References:

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