Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Finitely generated non-Hopfian groups

Author: A. H. Rhemtulla
Journal: Proc. Amer. Math. Soc. 81 (1981), 382-384
MSC: Primary 20E34; Secondary 20F99
MathSciNet review: 597645
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss finitely generated groups that are badly non-Hopfian. Given any countable group $ L$, we construct a finitely generated group $ G = K \times H$ where $ H$ is isomorphic to $ G$ and $ L$ is a two-step subnormal subgroup of $ K$.

References [Enhancements On Off] (What's this?)

  • [1] P. Hall, On the embedding of a given group in a join of given groups, J. Austral. Math. Soc. 17 (1974), 434-495. MR 0376880 (51:13055)
  • [2] -, Nilpotent groups, Canad. Math. Congress Summer Seminar, Univ. of Alberta, 1957.
  • [3] P. Neumann, Endomorphisms of infinite soluble groups, Bull. London Math. Soc. 12 (1980), 13-16. MR 565475 (81g:20071)
  • [4] J. M. Tyrer-Jones, Direct product and the Hopf property, J. Austral. Math. Soc. 17 (1974), 174-196. MR 0349855 (50:2348)
  • [5] J. S. Wilson, On characteristically simple groups, Math. Proc. Cambridge Philos. Soc. 80 (1976), 19-35. MR 0407156 (53:10939)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E34, 20F99

Retrieve articles in all journals with MSC: 20E34, 20F99

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society