Finite groups with ℙ-subnormal and strongly permutable subgroups

2021/08/16 by Виктор Степанович Монахов, Monakhov, V. S., Irina L. Sokhor +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2108.06993

openalex publication_date 2021/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a subgroup of a group G. The permutizer P_G(H) is the subgroup generated by all cyclic subgroups of G which permute with H. A subgroup H of a group G is strongly permutable in G if P_U(H)=U for every subgroup U of G such that~H≤ U≤ G. We investigate groups with ℙ-subnormal or strongly permutable Sylow and primary cyclic subgroups. In particular, we prove that groups with all strongly permutable primary cyclic subgroups are supersoluble.

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