On the Extraction of Roots in Exponential A-Groups II

Abstract

This is the second article by the authors on extraction of roots in exponential A-groups. We prove results on ω-torsion and ω-isolated subgroups, 𝒰_ω-groups, ℰ_ω-groups, and 𝒟_ω-groups in the category of exponential A-groups, where A is a unique factorization domain (UFD) and ω is a set of primes in A. In particular, we prove that every ω-torsion-free -group is a 𝒰_ω-group. We also prove that if R is a principal ideal domain (PID) and G is a finitely R-generated nilpotent R-powered group, then the R-subgroup of ω'-torsion elements of G equals its maximal ℰ_ω-subgroup (ω' denotes the set of primes in R not in ω).

Key Words:

• Exponential A-group
• Extraction of roots
• Nilpotent R-powered group
• Nilpotent R-group
• R-group

2000 Mathematics Subject Classification:

• Primary 20F18, 20F19
• Secondary 13C12, 13C13

ACKNOWLEDGMENT

The authors would like to thank the referee for his comments and suggestions.

The first-named author was supported by the PSC-CUNY Research Award Program (Grant # 62302)

Notes

Communicated by A. Olslanskii.