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Articles

Finite groups with some σ-primary subgroups -quasinormal

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Pages 5501-5510 | Received 23 Apr 2020, Accepted 29 Jun 2020, Published online: 21 Jul 2020
 

Abstract

Let G be a finite group, σ={σi|iI} a partition of the set of all primes P and σ(G)={σi|σiπ(|G|)}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every nonidentity member of H is a Hall σi-subgroup of G for some iI and H contains exactly one Hall σi-subgroup of G for every σiσ(G). G is said to be σ-full if G possesses a complete Hall σ-set. We say a subgroup H of G is sσ-quasinormal (supplement-σ-quasinormal) in G if there exists a σ-full subgroup T of G such that G = HT and H permutes with every Hall σi-subgroup of T for all σiσ(T). In this article, we obtain some results about the -quasinormal subgroups and use them to determine the structure of finite groups. In particular, some new criteria of p-nilpotency, solubility, supersolubility of a group are obtained.

MATHEMATICS SUBJECT CLASSIFICATION:

Additional information

Funding

Research was supported by the NNSF of China (11771409) and Anhui Initiative in Quantum Information Technologies (AHY150200).

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