The Conjugacy Problem in Amalgamated Products I: Regular Elements and Black Holes
Abstract
We discuss the time complexity of the word and conjugacy search problems for free products G = A C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups A,B,C.
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