The conjugacy problem for HNN extensions with infinite cyclic associated groups

Authors:
K. J. Horadam and G. E. Farr

Journal:
Proc. Amer. Math. Soc. **120** (1994), 1009-1015

MSC:
Primary 20F10; Secondary 20E06, 20M18

DOI:
https://doi.org/10.1090/S0002-9939-1994-1185267-4

MathSciNet review:
1185267

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Abstract | References | Similar Articles | Additional Information

Abstract: Under suitable recursive conditions, the conjugacy problem for HNN extensions of the form is solvable if and only if the inverse subsemigroup generated by has solvable extended word problem in the semigroup

Furthermore, is isomorphic to the direct sum of countably many copies of the *bicyclic* semigroup, which has a central place in the theory of inverse semigroups.

This new approach to the conjugacy problem is used to determine several classes of HNN extensions with infinitely many stable letters and solvable conjugacy problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1185267-4

Keywords:
Conjugacy problem,
HNN extension,
extended word problem,
inverse semigroup,
bicyclic semigroup

Article copyright:
© Copyright 1994
American Mathematical Society