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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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Conjugacy separability of certain free products with amalgamation
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by Peter F. Stebe PDF
Trans. Amer. Math. Soc. 156 (1971), 119-129 Request permission

Abstract:

Let G be a group. An element g of G is called conjugacy distinguished or c.d. in G if and only if given any element h of G either h is conjugate to g or there is a homomorphism $\xi$ from G onto a finite group such that $\xi (h)$ and $\xi (g)$ are not conjugate in $\xi (G)$. Following A. Mostowski, a group G is conjugacy separable or c.s. if and only if every element of G is c.d. in G. In this paper we prove that every element conjugate to a cyclically reduced element of length greater than 1 in the free product of two free groups with a cyclic amalgamated subgroup is c.d. We also prove that a group formed by adding a root of an element to a free group is c.s.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 156 (1971), 119-129
  • MSC: Primary 20.52
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0274597-5
  • MathSciNet review: 0274597