Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the combinatorial derivation of non-small sets   Given an infinite group $G$ and a subset $A$ of $G$ we let $\Delta(A) = \{g
\in G \,:\, |gA \cap A| =\infty\}$ (this is sometimes called the
\emph{combinatorial derivation} of $A$). A subset $A$ of $G$ is called:
\emph{large} if there exists a finite subset $F$ of $G$ such that $FA=G$;
\emph{$\Delta$-large} if $\Delta(A)$ is large and \emph{small} if for every
large subset $L$ of $G$, $(G \setminus A) \cap L$ is large. In this note we
show that every non-small set is $\Delta$-large, answering a question of
Protasov.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga