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On Keller's conjecture for certain cyclic groups

Published online by Cambridge University Press:  20 January 2009

A. D. Sands
A. D. Sands
Affiliation:
The UniversityDundeeScotland
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Keller (6) considered a generalisation of a problem of Minkowski (7) concerning the filling of Rn by congruent cubes. Hajós (4) reduced Minkowski's conjecture to a problem concerning the factorization of finite abelian groups and then solved this problem. In a similar manner Hajós (5) reduced Keller's conjecture to a problem in the factorization of finite abelian groups, but this problem remains unsolved, in general. It occurs also as Problem 80 in Fuchs (3). Seitz (10) has obtained a solution for cyclic groups of prime power order. In this paper we present a solution for cyclic groups whose order is the product of two prime powers.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 1 , February 1979 , pp. 17 - 21
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

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