Abstract
A subgroup H of a finite group G is called ℙ-subnormal in G whenever H either coincides with G or is connected to G by a chain of subgroups of prime indices. If every Sylow subgroup of G is ℙ-subnormal in G then G is called a w-supersoluble group. We obtain some properties of ℙ-subnormal subgroups and the groups that are products of two ℙ-subnormal subgroups, in particular, of ℙ-subnormal w-supersoluble subgroups.
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Original Russian Text Copyright © 2012 Vasil’ev A. F., Vasil’eva T. I., and Tyutyanov V. N.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 1, pp. 59–67, January–February, 2012.
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Vasil’ev, A.F., Tyutyanov, V.N. & Vasil’eva, T.I. On the products of ℙ-subnormal subgroups of finite groups. Sib Math J 53, 47–54 (2012). https://doi.org/10.1134/S0037446612010041
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DOI: https://doi.org/10.1134/S0037446612010041