Geodesic
The Herzog-Schönheim Conjecture for Finite Nilpotent Groups
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 329-333

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this note is to prove the Herzog-Schônheim [3] conjecture for finite nilpotent groups. This conjecture states that any nontrivial partition of a group into cosets must contain two cosets of the same index (Corollary IV below). See Porubský [4, Section 8] for a perspective on coset partitions.
DOI : 10.4153/CMB-1986-050-0
Mots-clés : 05A17, 10A45, 20DI5, 20D60, coset partition, Euler φ-function, nilpotent group 
Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri. The Herzog-Schönheim Conjecture for Finite Nilpotent Groups. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 329-333. doi: 10.4153/CMB-1986-050-0
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[1] 1. Berger M., A., Felzenbaum, A. and Fraenkel, A., Lattice parallelepipeds and disjoint covering systems, Discrete Math, (in press). Google Scholar

[2] 2. Burshtein, N., On natural covering systems of congruences having moduli occurring at most M times, Discrete Math. 14(1976), pp. 205–214. Google Scholar

[3] 3. Herzog, M. and Schônheim, J., Research problem No. 9, Canad. Math. Bull. 17(1974), p. 150 Google Scholar

[4] 4. Porubský, S., Results and problems on covering systems of residue classes, Mitteilungen aus dem Math. Sem. Giessen, Heft 150, Giessen Univ., 1981. Google Scholar

[5] 5. Rotman J., J., The Theory of Groups: An Introduction, Allyn and Bacon, Boston, 1973. Google Scholar

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