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, 𝒰ω-groups, ℰω-groups, and 𝒟ω-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 𝒰ω-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 ℰω-subgroup (ω' denotes the set of primes in R not in ω).
2000 Mathematics Subject Classification:
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.