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- Title
On finitely generated soluble non-Hopfian groups.
- Authors
Mikaelian, Vahagn H.
- Abstract
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 uncountably many pairwise nonisomorphic finitely generated groups.
- Subjects
NON-Hopfian groups; NEUMANN problem; MATHEMATICAL continuum; SOLVABLE groups; GROUP theory; AUTOMORPHISMS
- Publication
Journal of Mathematical Sciences, 2010, Vol 166, Issue 6, p743
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-010-9890-4