On Subsets of Finite Abelian Groups without Non-trivial Solutions
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چکیده
Let D(G) be the maximal cardinality of a set A ⊆ G that contains no non-trivial solution to x1 + · · · + xs − sxs+1 = 0 with xi ∈ A (1 ≤ i ≤ s + 1). Let d(n) = sup rk(H)≥n D(H) |H| , where rk(H) is the rank of H. We prove that for any n ∈ N, d(n) ≤ C ns−2 , where C is a fixed constant depending only on s.
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