Pairwise -connected Products of Certain Classes of Finite Groups

Abstract

Subgroups A and B of a finite group are said to be 𝒩-connected if the subgroup generated by elements x and y is a nilpotent group, for every pair of elements x in A and y in B. The behaviour of finite pairwise permutable and 𝒩-connected products are studied with respect to certain classes of groups including those groups where all the subnormal subgroups permute with all the maximal subgroups, the so-called SM-groups, and also the class of soluble groups where all the subnormal subgroups permute with all the Carter subgroups, the so-called C-groups.

Key Words:

• Finite group
• PST-group
• Supersoluble
• 𝒩-connected

2000 Mathematics Subject Classification:

• 20D10
• 20D15

Acknowledgment

The authors were supported in part by NATO grant CRG 970091.

Notes

^#Communicated by M. Dixon.