Periodica Mathematica Hungarica

, Volume 17, Issue 4, pp 265–277

A reduction of Keller's conjecture

  • S. Szabó

DOI: 10.1007/BF01848388

Cite this article as:
Szabó, S. Period Math Hung (1986) 17: 265. doi:10.1007/BF01848388


A family of translates of a closedn-dimensional cube is called a cube tiling if the union of the cubes is the wholen-space and their interiors are disjoint. According to a famous unsolved conjecture of O. H. Keller, two of the cubes in ann-dimensional cube tiling must share a complete (n − 1)-dimensional face. In this paper we shall prove that to solve Keller's conjecture it is sufficient to examine certain factorizations of direct sum of finitely many cyclic group of order four.

AMS (MOS) subject classifications (1980)

Primary 10E30 Secondary 20K01, 52A45 

Key words and phrases

Cube tiling factorization of abelian groups 

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • S. Szabó
    • 1
  1. 1.Budapesti Műszaki EgyetemÉpítómérnöki Kar Matematikai TanszékBudapestHungary

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