Home / Publications / Published articles / Algorithmic problems for free-abelian times free groups

Jordi Delgado and Enric Ventura (2013)

Algorithmic problems for free-abelian times free groups

Journal of Algebra, 391:256–283.

Abstract We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of Z m × F n . These tools are used to solve several algorithmic problems for Z m × F n : the membership problem, the isomorphism problem, the finite index problem, the subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem.

Free-abelian group, Decision problem, Free group, Automorphism