FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 1, PAGES 81-98

**On finitely generated soluble non-Hopfian groups**

V. H. Mikaelian

Abstract

View as HTML
View as gif image

There is a continuum of $3$-generator soluble
non-Hopfian groups that generate pairwise distinct varieties of
groups.
Each countable (soluble) group is subnormally embeddable into
a $3$-generator (soluble)
non-Hopfian group.
As an illustration to a problem of Neumann, we find
a continuum of nonmetanilpotent varieties that contain finitely
generated non-Hopfian groups and contain noncountably many pairwise
nonisomorphic finitely generated groups.

Location: http://mech.math.msu.su/~fpm/eng/k09/k091/k09106h.htm

Last modified: December 2, 2009