Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 464.20034
Autor: Erdös, Paul; Smith, B.
Title: Finite Abelian group cohesion. (In English)
Source: Isr. J. Math. 39, 177-185 (1981).
Review: Let G be a finite Abelian group with \#G = p. For A,b\subset G let m(x,A,B) = \#{(a,b): a+b = x,a in A,b in B}. For E\subset G let E' denote its complement. The authors prove the following results: sumc in G |m(x,E,E)+m(x,E',E')-m(x,E,E')-m(x,E',E)|2 =
sumc in G |m(x,E,-E)+m(x,E',-E')-m(x,E,-E')-m(x,E',-E)|2 (i) (Cohesion equation)
maxE\subset Gmaxx in G|m(x,E,E)+m(x,E',E')-2m(x,E,E')| \geq p ½ (ii) If \lambda > ½ and G contains no element of order 2, then
maxE\subset Gmaxx in G|m(x,E,E)+m(x,E',E')-2m(x,E,E')| \geq K.p\lambda (iii) Here K depends only on \lambda.
Reviewer: St.Porubský
Classif.: * 20K01 Finite abelian groups
20D60 Arithmetic and combinatorial problems on finite groups
11P99 Additive number theory
20P05 Probability methods in group theory
11B05 Topology etc. of sets of numbers
Keywords: finite Abelian group; sum set; Cohesin equation
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