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


Joshua Erde

A note on the combinatorial derivation of nonsmall sets

view    print

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

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