Asymmetric decompositions of abelian groups |
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Authors: | T. O. Banach I. V. Protasov |
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Affiliation: | (1) I. Franko Lvov State University, Lvov, USSR;(2) T. Shevchenko Kiev State University, Kiev, USSR |
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Abstract: | A subsetA of an Abelian groupG is said to be asymmetric ifg+S⊄A for any elementg∈G and any infinite symmetric subsetS⊂G (S=−S). The minimal cardinality of a decomposition of the groupG into asymmetric sets is denoted by ν(G). for any Abelian groupG, the cardinal number ν(G is expressed via the following cardinal invariants: the free rank, the 2-rank, and the cardinality of the group. In particular, . Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 10–19, July, 1999. |
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Keywords: | Abelian group asymmetric set asymmetric decomposition free rank 2-rank |
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