Abstract
We prove that the Brinkmann Problems ( BrP & BrCP ) and the Twisted-Conjugacy Problem ( TCP ) are decidable for any endomorphism of a free-abelian times free (FATF) group [Formula: see text]. Furthermore, we prove the decidability of the two-sided Brinkmann Conjugacy Problem ( 2BrCP ) for monomorphisms of FATF groups (and combine it with TCP ) to derive the decidability of the conjugacy problem for ascending HNN extensions of FATF groups.
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