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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Splitting groups by integers


Authors: W. Hamaker and S. Stein
Journal: Proc. Amer. Math. Soc. 46 (1974), 322-324
MSC: Primary 20K25
DOI: https://doi.org/10.1090/S0002-9939-1974-0349874-8
MathSciNet review: 0349874
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Abstract: A question concerning tiling Euclidean space by crosses raised this algebraic question: Let $ G$ be a finite abelian group and $ S$ a set of integers. When do there exist elements $ {g_1},{g_2}, \cdots ,{g_n}$ in $ G$ such that each nonzero element of $ G$ is uniquely expressible in the form $ s{g_i}$ for some $ s$ in $ S$ and some $ {g_i}$? The question is answered for a broad (but far from complete) range of $ S$ and $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0349874-8
Keywords: Exact sequence, abelian group, splitting
Article copyright: © Copyright 1974 American Mathematical Society