 

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 


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; Δlarge 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 Δlarge, answering a question of Protasov.


Author information
DPMMS, University of Cambridge
joshua.erde@unihamburg.de

