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Sums of Complexes in Torsion-Free Abelian Groups
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1969
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