Non-Hopfian groups with fully invariant kernels. I
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- by Michael Anshel PDF
- Trans. Amer. Math. Soc. 170 (1972), 231-237 Request permission
Abstract:
Let $\mathcal {L}$ consist of the groups $G(l,m) = (a,b;{a^{ - 1}}{b^l}a = {b^m})$ where $|l| \ne 1 \ne |m|,lm \ne 0$ and $l,m$ are coprime. We characterize the endomorphisms of these groups, compute the centralizers of special elements and show that the endomorphism $a \to a,b \to {b^l}$ is onto with a nontrivial fully invariant kernel. Hence $G(l,m)$ is non-Hopfian in the’fully invariant sense.’References
- Michael Anshel, The endomorphisms of certain one-relator groups and the generalized Hopfian problem, Bull. Amer. Math. Soc. 77 (1971), 348–350. MR 272876, DOI 10.1090/S0002-9904-1971-12688-5 Michael Anshel (Orleck), Non-Hopfian groups with fully invariant kernels, Ph.D. Thesis, Adelphi University, Garden City, N.Y., 1967.
- Gilbert Baumslag and Donald Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199–201. MR 142635, DOI 10.1090/S0002-9904-1962-10745-9
- Gilbert Baumslag, Residually finite one-relator groups, Bull. Amer. Math. Soc. 73 (1967), 618–620. MR 212078, DOI 10.1090/S0002-9904-1967-11799-3
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 170 (1972), 231-237
- MSC: Primary 20F05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0304491-3
- MathSciNet review: 0304491