Geodesic
Sums of Complexes in Torsion-Free Abelian Groups
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 475-478

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

The number of elements in the sum A + B of two complexes A and B of a group G which have multiple representations a + b = a '+ b' has been investigated by Scherk and Kemperman [1]. Kemperman [2] appealed to transfinite techniques (to order G) to prove: If G is a torsion-free abelian group with finite subsets A and B with | B | ≥ 2, then at least two elements c of A + B admit exactly one representation c = a + b. 
Tarwater, J. D.; Entringer, R. C. Sums of Complexes in Torsion-Free Abelian Groups. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 475-478. doi: 10.4153/CMB-1969-060-4
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[1] 1. Scherk, P. and Kemperman, J. H. B., Complexes in abelian groups. Canad. J. Math. 6 (1954) 230–237. Google Scholar

[2] 2. Kemperman, J. H. B., On complexes in a semigroup. Indag. Math. 18 (1956) 247–254. Google Scholar

[3] 3. Entringer, R. C., The 2Ω. property of torsion-free abelian groups. Amer. Math. Monthly 74 (1967) 301–302. Google Scholar

[4] 4. Fuchs, L., Abelian groups. (Pergamon Press, Oxford, 1960.) Google Scholar

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