On cyclic subgroups and the conjugacy problem

Author:
R. Daniel Hurwitz

Journal:
Proc. Amer. Math. Soc. **79** (1980), 1-8

MSC:
Primary 20F10; Secondary 03D40

MathSciNet review:
560573

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Abstract: The conjugacy problem in three types of group constructions involving cyclic subgroups is discussed. First it is shown that if *G* has the solvable conjugacy problem and if and satisfy (a) *h* and *k* are not power conjugate to themselves or each other, (b) the power conjugacy problem in *G* with respect to *h* or *k* is solvable, and (c) the double coset solvability problem in *G* is solvable with respect to and , then the HNN extension has the solvable conjugacy problem. This result is used to deduce a similar theorem for free products with amalgamation, a fact first stated by Lipschutz. Then it is shown that if *A* and *B* are groups with the solvable conjugacy problem and and taken with themselves satisfy the conditions above in *A* and *B*, respectively, then has the solvable conjugacy problem.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0560573-2

Article copyright:
© Copyright 1980
American Mathematical Society