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Constructions Related to the Rédei Property of Groups
Author(s) -
Szabó Sándor
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022861
Subject(s) - abelian group , property (philosophy) , mathematics , group (periodic table) , identity (music) , combinatorics , order (exchange) , product (mathematics) , finite group , pure mathematics , physics , geometry , philosophy , epistemology , finance , quantum mechanics , acoustics , economics
We say that a finite abelian group does not have the Rédei property if it can be expressed as a direct product of two of its subsets such that both subsets contain the identity element and both subsets span the whole group. It will be shown that only a small fraction of the finite abelian groups can have the Rédei property. For groups of odd order an explicit list of the possible exceptions is compiled.