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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the finite images of some one-relator groups
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by D. Moldavanski and N. Sibyakova
Proc. Amer. Math. Soc. 123 (1995), 2017-2020
DOI: https://doi.org/10.1090/S0002-9939-1995-1273511-5

Abstract:

It is shown that the group $G = \langle a,b;{a^{ - 1}}ba = {b^k}\rangle (k \ne 0)$ is determined in the class of all residually finite one-relator groups by the set of its finite images.
References
  • Gilbert Baumslag, Residually finite groups with the same finite images, Compositio Math. 29 (1974), 249–252. MR 357615
  • Martin D. Burrow and Arthur Steinberg, On a result of G. Baumslag, Compositio Math. 71 (1989), no. 3, 241–245. MR 1022043
  • W. Magnus, Uber diskontinuierliche gruppen mit einer definieren den relation (der Freiheitssatz), J. Reine Angew. Math. 163 (1930), 141-165.
  • Gilbert Baumslag, Some problems on one-relator groups, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Lecture Notes in Math., Vol. 372, Springer, Berlin, 1974, pp. 75–81. MR 0364463
  • Gilbert Baumslag, A non-cyclic one-relator group all of whose finite quotients are cyclic, J. Austral. Math. Soc. 10 (1969), 497–498. MR 0254127, DOI 10.1017/S1446788700007783
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2017-2020
  • MSC: Primary 20F05; Secondary 20E26
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1273511-5
  • MathSciNet review: 1273511