On the removal lemma for linear systems over Abelian groups |
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Authors: | Daniel Král’ Oriol Serra Lluís Vena |
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Institution: | 1. Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Czech Republic;2. Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Spain;3. Department of Mathematics, University of Toronto, Canada |
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Abstract: | In this paper we present an extension of the removal lemma to integer linear systems over abelian groups. We prove that, if the k-determinantal of an integer (k×m) matrix A is coprime with the order n of a group G and the number of solutions of the system Ax=b with x1∈X1,…,xm∈Xm is o(nm−k), then we can eliminate o(n) elements in each set to remove all these solutions. |
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