A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression
Abstract
Let r1, . . . , rs be non-zero integers satisfying r1 + · · · + rs = 0. Let G
Z/k1Z⊕· · ·⊕Z/knZ be a finite abelian group with ki |ki−1(2 ≤ i ≤ n), and suppose that
(ri , k1) = 1(1 ≤ i ≤ s). Let Dr(G) denote the maximal cardinality of a set A ⊆ G which
contains no non-trivial solution of r1x1+· · · +rs xs = 0 with xi ∈ A(1 ≤ i ≤ s).We prove
that Dr(G) |G|/ns−2. We also apply this result to study problems in finite projective
spaces.
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Cite this version of the work
Yu-Ru Liu, Craig V. Spencer
(2009).
A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression. UWSpace.
http://hdl.handle.net/10012/19999
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