Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Conjugacy separability of certain free products with amalgamation


Author: Peter F. Stebe
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] S. Lipshutz, Generalization of Dehn's result on the conjugacy problem, Proc. Amer. Math. Soc. 17 (1966), 759-762. MR 33 #5706. MR 0197541 (33:5706)
  • [2] A. Karrass and D. Solitar, On finitely generated subgroups of a free group, Proc. Amer. Math. Soc. 22 (1969), 209-213. MR 39 #6961. MR 0245655 (39:6961)
  • [3] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617.
  • [4] A. W. Mostowski, On the decidability of some problems in special classes of groups, Fund. Math. 59 (1966), 123-135. MR 37 #292. MR 0224693 (37:292)
  • [5] B. H. Neumann, An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503-554. MR 16, 10. MR 0062741 (16:10d)
  • [6] A. Speiser, Theorie der Gruppen von endlicher Ordnung, 3rd ed., Springer, Berlin, 1936.
  • [7] P. Stebe, A residual property of certain groups, Proc. Amer. Math. Soc. 26 (1970), 37-42. MR 0260874 (41:5494)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20.52

Retrieve articles in all journals with MSC: 20.52


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0274597-5
Keywords: Group, conjugacy problem, conjugacy separable group, free product with amalgamation
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society