On Subsets of Finite Abelian Groups with Arithmetic Progressions
نویسنده
چکیده
Brown and Buhler [ 3 ] and F rank l , G r a h a m and R6dl [ 4 ] p roved tha t D(G) = o(IG I) for all G (here, and t h r o u g h o u t the pape r G denotes a finite abe l ian g roup of odd order) . In this no te we are in teres ted in D(G) for g roups with m a n y const i tuents . A lon and D u b i n e r [ 1, 2] asked whether there exists a cons tan t c < 3 such tha t D(Z~)~<c". I. Ruzsa has recent ly p roved tha t D ( Z ~ ) = o ( 3 n / x / ~ ) (pr ivate c o m m u n i c a t i o n f rom N. Alon) .
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تاریخ انتشار 2004