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Propermutable characterizations of finite soluble PST-Groups and PT-groups

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Abstract

Let H and X be subgroups of a group G. We say that a subgroup H is X-propermutable in G provided that there is a subgroup B of G such that G = N G (H)B and H X-permutes (in the sense of [1]) with all subgroups of B. In this paper we analyze the influence of X-propermutable subgroups on the structure of a finite group G. In particular, it is proved that G is a soluble PST-group if and only if all Hall subgroups and all maximal subgroups of every Hall subgroup of G are X-propermutable in G, where X = Z ∞(G).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, P. R. China

    X. Yi

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  1. X. Yi
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Correspondence to X. Yi.

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Hangzhou. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 2, pp. 377–388, March–April, 2015.

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Yi, X. Propermutable characterizations of finite soluble PST-Groups and PT-groups. Sib Math J 56, 304–312 (2015). https://doi.org/10.1134/S003744661502010X

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  • DOI: https://doi.org/10.1134/S003744661502010X

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