New York Journal of Mathematics Volume 20 (2014) 921-925
 Volume 20 Volume Index

Joshua Erde

A note on the combinatorial derivation of nonsmall sets

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 Published: October 14, 2014 Keywords: Subset combinatorics of groups, combinatorial derivation, large and small subsets of groups Subject: 05E15

Abstract
Given an infinite group G and a subset A of G we let
Δ(A) = {g ∈ G : |gA ∩ A|=∞}
(this is sometimes called the combinatorial derivation of A). A subset A of G is called: large if there exists a finite subset F of G such that FA=G; Δ-large if Δ(A) is large and small if for every large subset L of G, (G \setminus A) ∩ L is large. In this note we show that every nonsmall set is Δ-large, answering a question of Protasov.

Author information

DPMMS, University of Cambridge
joshua.erde@uni-hamburg.de