On σ-conditionally permutable subgroups of finite groups

Abstract

Let σ be some partition of the set of all primes and $\mathcal{H}$ a complete Hall σ-set of a finite group G. A subgroup H of G is said to be σ-conditionally permutable in G if for any subgroup $A\in \mathcal{H},$ there exists an element $x\in G$ such that $H{A}^x=A^{x}H.$ In this article, we investigate the influence of σ-conditionally permutable subgroups on the structure of finite groups.

Keywords:

• Finite groups
• σ-soluble groups
• σ-conditionally permutable subgroups
• structure of finite groups
• supersoluble groups

Mathematics Subject Classification (2010):

• 20D10
• 20D20
• 20D35

Additional information

Funding

Research is supported by a NNSF grant of China (Grant no. 11771409) and Anhui Initiative in Quantum Information Technologies (No. AHY150200).