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On a conjecture of G. Hajós

1974
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Glasgow Mathematical Journal
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1. Introduction. The purpose of this note is to provide by means of an example a negative answer to a conjecture of Haj6s [3] concerning the factorization of finite abelian groups. This question is also raised as Problem 81 in Fuchs [2]. If S, T are subsets of an additive abelian group G their sum S+ T is said to be direct if s t + t x = s 2 +1 2 implies s t = s 2 , t x = t 2 , where s t e S, t t e T. If the sum is direct and S+ T = G, then we have a factorization of G. All sums considered in

doi:10.1017/s0017089500002202
fatcat:2hhqpywgsfbk5n3jg6ndwhsrs4