The conjugacy problem for graph products with infinite cyclic edge groups

Lockhart, Jody Meyer

doi:10.1090/S0002-9939-1992-1072088-4

The conjugacy problem for graph products with infinite cyclic edge groups
HTML articles powered by AMS MathViewer

by Jody Meyer Lockhart

Proc. Amer. Math. Soc. 114 (1992), 603-606

DOI: https://doi.org/10.1090/S0002-9939-1992-1072088-4

PDF | Request permission

Abstract:

Finite graph products of groups with solvable conjugacy problem and infinite cyclic edge groups are considered. It is shown that the graph product has solvable conjugacy problem if the images of the edge group generators in each vertex group ${G_v}$ are powers of a common central element $c$, where the group generated by $c$ has solvable generalized word problem in ${G_v}$.

References

K. J. Horadam, The conjugacy problem for graph products with central cyclic edge groups, Proc. Amer. Math. Soc. 91 (1984), no. 3, 345–350. MR 744626, DOI 10.1090/S0002-9939-1984-0744626-5
K. J. Horadam, The conjugacy problem for finite graph products, Proc. Amer. Math. Soc. 106 (1989), no. 3, 589–592. MR 962244, DOI 10.1090/S0002-9939-1989-0962244-5
R. Daniel Hurwitz, On cyclic subgroups and the conjugacy problem, Proc. Amer. Math. Soc. 79 (1980), no. 1, 1–8. MR 560573, DOI 10.1090/S0002-9939-1980-0560573-2
Seymour Lipschutz, The conjugacy problem and cyclic amalgamations, Bull. Amer. Math. Soc. 81 (1975), 114–116. MR 379675, DOI 10.1090/S0002-9904-1975-13661-5
Jody Meyer Lockhart, An HNN-extension with cyclic associated subgroups and with unsolvable conjugacy problem, Trans. Amer. Math. Soc. 313 (1989), no. 1, 331–345. MR 992601, DOI 10.1090/S0002-9947-1989-0992601-7
Charles F. Miller III, On group-theoretic decision problems and their classification, Annals of Mathematics Studies, No. 68, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0310044
Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504