2,242 research outputs found

    Algorithmic recognition of infinite cyclic extensions

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    We prove that one cannot algorithmically decide whether a finitely presented Z\mathbb{Z}-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the equivalence between the isomorphism problem within the subclass of unique Z\mathbb{Z}-extensions, and the semi-conjugacy problem for deranged outer automorphisms.Comment: 24 page

    Knapsack problems in products of groups

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    The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsack-type problems in groups. We study the effect of free and direct products on their time complexity. We show that free products in certain sense preserve time complexity of knapsack-type problems, while direct products may amplify it. Our methods allow to obtain complexity results for rational subset membership problem in amalgamated free products over finite subgroups.Comment: 15 pages, 5 figures. Updated to include more general results, mostly in Section
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