This paper demonstrates independence among the conjugacy problem, dehn function, and conjugator length function in finitely generated groups, suggesting new avenues for research.
Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the Dehn function, and the conjugator length function. We furnish the theory with diverse examples groups. In particular, we show that these three invariants are independent -- no two of the three functions determine the other.
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Gillis et al. (2025) studied this question.
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