In the free-by-cyclic groups H_m defined by the polynomial-growth automorphism a_i -> a_i a_{i-1}, the conjugator length function is linear and the conjugacy and conjugacy-search problems have polynomial-time solutions.
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Conjugacy in a family of free-by-cyclic groups
In the free-by-cyclic groups H_m defined by the polynomial-growth automorphism a_i -> a_i a_{i-1}, the conjugator length function is linear and the conjugacy and conjugacy-search problems have polynomial-time solutions.