International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 539-544

On almost finitely generated nilpotent groups

Peter Hilton1,2 and Robert Militello3

1Department of Mathematical Sciences, State University of New York, Binghamton 13902-6000, NY, USA
2Department of Mathematics, University of Central Florida, Orlando 32816-6990, FL, USA
3Department of Mathematics, Rhodes College, Memphis 38112-1690, TN, USA

Received 3 October 1994

Copyright © 1996 Peter Hilton and Robert Militello. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 GpHp 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.