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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
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$.

References [Enhancements On Off] (What's this?)

  • [1] W. Hamaker, Factoring groups and tiling space, Aequationes Math. 9 (1973), 145-149. MR 0327551 (48:5893)
  • [2] S. K. Stein, Factoring by subsets, Pacific J. Math. 22 (1967), 523-541. MR 36 #2517. MR 0219435 (36:2517)
  • [3] -, A symmetric star body that tiles but not as a lattice, Proc. Amer. Math. Soc. 36 (1972), 543-548. MR 0319058 (47:7604)

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Keywords: Exact sequence, abelian group, splitting
Article copyright: © Copyright 1974 American Mathematical Society

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