On factorized groups with permutable subgroups of factors

2020/05/19 by Monakhov, Victor S., Trofimuk, Alexander A.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2005.09277

Abstract

The subgroups A and B of a group~G are called \rm msp-permutable, if the following statements hold: AB~is a subgroup of~G; the subgroups P and Q are mutually permutable, where P~is an arbitrary Sylow p-subgroup of~A and Q~is an arbitrary Sylow q-subgroup of~B, p≠ q. In the present paper, we investigate groups that factorized by two \rm msp-permutable subgroups. In particular, the supersolubility of the product of two supersoluble \rm msp-permutable subgroups is proved.

Related

• Finite groups with ℙ-subnormal and strongly permutable subgroups
• On permutizers of subgroups of finite groups
• On the supersoluble residual of mutually permutable products
• On some products of finite groups
• On a generalization of the concept of S-permutable subgroup of a finite group