Some one-relator Hopfian groups
Author:
Donald J. Collins
Journal:
Trans. Amer. Math. Soc. 235 (1978), 363-374
MSC:
Primary 20E30
DOI:
https://doi.org/10.1090/S0002-9947-1978-0460468-4
MathSciNet review:
0460468
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Abstract: The group presented by \[ (a,t;{t^{ - 1}}{a^l}t = {a^m})\] is non-Hopfian if $l,m \ne \pm 1$ and $\pi (l) \ne \pi (m)$, where $\pi (l)$ and $\pi (m)$ denote the sets of prime divisors of l and m. By contrast, we prove that if w is a word of the free group $F({a_1},{a_2})$ which is not primitive and not a proper power, then the group $({a_1},{a_2},t;{t^{ - 1}}{w^l}t = {w^m})$ is Hopfian.
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© Copyright 1978
American Mathematical Society