On cyclic subgroups and the conjugacy problem
Author:
R. Daniel Hurwitz
Journal:
Proc. Amer. Math. Soc. 79 (1980), 18
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:
http://dx.doi.org/10.1090/S00029939198005605732
PII:
S 00029939(1980)05605732
Article copyright:
© Copyright 1980
American Mathematical Society
