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arXiv · 1301.2355

Algorithmic problems for free-abelian times free groups

J. Delgado·E. Ventura
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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 $\ZZ^m \times F_n$. These tools are used to solve several algorithmic and decision problems for $\ZZ^m \times 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.

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J. Delgado, E. Ventura. 2013-01-10. Algorithmic problems for free-abelian times free groups. https://arxiv.org/abs/1301.2355

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