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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.’
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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