Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattered Subsets of Groups   We define the scattered subsets of a group as asymptotic counterparts of
scattered subspaces of a topological space, and prove that a subset $A$ of a
group $G$ is scattered if and only if $A$ contains no piecewise shifted
$IP$-subsets. For an amenable group $G$ and a scattered subspace $A$ of $G$, we
show that $\mu(A)=0$ for each left invariant Banach measure $\mu$ on $G$.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci