Finitely generated non-Hopfian groups
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- by A. H. Rhemtulla PDF
- Proc. Amer. Math. Soc. 81 (1981), 382-384 Request permission
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
- P. Hall, On the embedding of a group in a join of given groups, J. Austral. Math. Soc. 17 (1974), 434–495. Collection of articles dedicated to the memory of Hanna Neumann, VIII. MR 0376880 —, Nilpotent groups, Canad. Math. Congress Summer Seminar, Univ. of Alberta, 1957.
- Peter M. Neumann, Endomorphisms of infinite soluble groups, Bull. London Math. Soc. 12 (1980), no. 1, 13–16. MR 565475, DOI 10.1112/blms/12.1.13
- J. M. Tyrer Jones, Direct products and the Hopf property, J. Austral. Math. Soc. 17 (1974), 174–196. Collection of articles dedicated to the memory of Hanna Neumann, VI. MR 0349855
- J. S. Wilson, On characteristically simple groups, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 1, 19–35. MR 407156, DOI 10.1017/S0305004100052622
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 382-384
- MSC: Primary 20E34; Secondary 20F99
- DOI: https://doi.org/10.1090/S0002-9939-1981-0597645-3
- MathSciNet review: 597645