A Characterization of Root Classes of Groups

Abstract

We prove that a class of groups is root in a sense of K. W. Gruenberg if, and only if, it is closed under subgroups and Cartesian wreath products. Using this result we obtain a condition which is sufficient for the generalized free product of two nilpotent groups to be residual solvable.

Key Words:

• Generalized free product
• Nilpotent group
• Residual solvability
• Root class of groups

2010 Mathematics Subject Classification:

• Primary: 20E22
• Secondary: 20E26
• 20E06
• 20F18

Notes

Communicated by A. Olshanskii.