On sub-class sizes of mutually permutable products

Abstract

In this paper, we investigate the influence of sub-class sizes on a mutually permutable factorized group in which the sub-class sizes of some elements of its factors have certain quantitative properties. Some criteria for a group to be pp-nilpotent or pp-supersolvable are given.

Keywords

• finite groups
• sub-class sizes
• mutually permutable products
• 20d10
• 20d20
• 20d40
• 20e45