On cyclic subgroups and the conjugacy problem
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- by R. Daniel Hurwitz PDF
- Proc. Amer. Math. Soc. 79 (1980), 1-8 Request permission
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 $h \in G$ and $k \in G$ 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 $\langle h\rangle$ and $\langle k\rangle$, then the HNN extension ${G^ \ast } = \langle G,t;{t^{ - 1}}ht = k\rangle$ 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 $h \in A$ and $k \in B$ taken with themselves satisfy the conditions above in A and B, respectively, then $\langle A ^\ast B;[h,k] = 1\rangle$ has the solvable conjugacy problem.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 1-8
- MSC: Primary 20F10; Secondary 03D40
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560573-2
- MathSciNet review: 560573