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

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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.

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Last modified: December 2, 2009