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- W2739516390 abstract "Summary Let G be an infinite abelian group withj2GjDjGj. We show that if G is not the direct sum of a group of exponent3 and the group of order2 ,t henG possesses a perfect additive basis; that is, there is a subset SG such that every element ofG is uniquely representable as a sum of two elements ofS . Moreover, if G is the direct sum of a group of exponent3 and the group of order2, then it does not have a perfect additive basis; however, in this case, there exists a basisSG such that every element of G has at most two representations (distinct under per- muting the summands) as a sum of two elements of S. This solves completely the Erd˝ os-Turan problem for infinite groups. It is also shown that ifG is an abelian group of exponent2, then there is a subset SG such that every element of G has a representation as a sum of two ele- ments of S , and the number of representations of nonzero elements is bounded by an absolute constant." @default.
- W2739516390 created "2017-08-08" @default.
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- W2739516390 date "2010-01-01" @default.
- W2739516390 modified "2023-09-27" @default.
- W2739516390 title "an Problem in Infinite Groups" @default.
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