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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some finitely presented non-$3$-manifold groups
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by Wolfgang H. Heil
Proc. Amer. Math. Soc. 53 (1975), 497-500
DOI: https://doi.org/10.1090/S0002-9939-1975-0438320-2

Abstract:

For every pair of integers $(m,n)$, G. Baumslag and D. Solitar exhibited two-generator one-relator groups ${G_{m,n}}$ that are not residually finite or Hopfian. It is shown that these groups do not provide counterexamples to the conjecture that $3$-manifold groups are residually finite (or at least Hopfian) by showing that they have subgroups which are not $3$-manifold groups.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 497-500
  • MSC: Primary 55A05; Secondary 57A10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0438320-2
  • MathSciNet review: 0438320