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We prove that the Brinkmann Problems (BrP & BrCP) and the twisted-conjugacyProblem (TCP) are decidable for any endomorphism of a free-abelian times free(FATF) group Fn x Z^m. Furthermore, we prove the decidability of the two-sidedBrinkmann conjugacy problem (2BrCP) for monomorphisms of FATF groups (andcombine it with TCP) to derive the decidability of the conjugacy problem forascending HNN extensions of FATF groups.

Orbit problems for free-abelian times free groups and related families