International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 539-544
doi:10.1155/S0161171296000749
On almost finitely generated nilpotent groups
Peter Hilton1
and Robert Militello2
1Department of Mathematical Sciences, State University of New York, Binghamton 13902-6000, NY, USA
2Department of Mathematics, Rhodes College, Memphis 38112-1690, TN, USA
Abstract
A nilpotent group G is fgp if Gp, is finitely generated (fg) as a p-local group for all primes p; it is fg-like if there exists a nilpotent fg group H such that Gp≃Hp for all primes p. The fgp nilpotent groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelian groups, a subgroup of an fg-like group is fg-like, and an extension of an fg-like group by an fg-like group is fg-like. These properties persist for nilpotent groups with finite commutator subgroup, but fail in general.