Splitting groups by integers
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- by W. Hamaker and S. Stein PDF
- Proc. Amer. Math. Soc. 46 (1974), 322-324 Request permission
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
- William Hamaker, Factoring groups and tiling space, Aequationes Math. 9 (1973), 145–149. MR 327551, DOI 10.1007/BF01832620
- S. K. Stein, Factoring by subsets, Pacific J. Math. 22 (1967), 523–541. MR 219435, DOI 10.2140/pjm.1967.22.523
- Sherman K. Stein, A symmetric star body that tiles but not as a lattice, Proc. Amer. Math. Soc. 36 (1972), 543–548. MR 319058, DOI 10.1090/S0002-9939-1972-0319058-6
Additional Information
- © Copyright 1974 American Mathematical Society
- 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