Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate subgroups of linear groups   We establish various results on the structure of approximate subgroups in
linear groups such as SL_n(k) that were previously announced by the authors.
For example, generalising a result of Helfgott (who handled the cases n = 2 and
3), we show that any approximate subgroup of SL_n(F_q) which generates the
group must be either very small or else nearly all of SL_n(F_q). The argument
generalises to other absolutely almost simple connected (and non-commutative)
algebraic groups G over a finite field k. In a subsequent paper, we will give
applications of this result to the expansion properties of Cayley graphs.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org