Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diameters of Cayley graphs of SL_n(Z/kZ)   We show that for integers k > 1 and n > 2, the diameter of the Cayley graph
of SL_n(Z/kZ) associated to a standard two-element generating set, is at most a
constant times n^2 ln k. This answers a question of A. Lubotzky concerning
SL_n(F_p) and is unexpected because these Cayley graphs do not form an expander
family. Our proof amounts to a quick algorithm for finding short words
representing elements of SL_n(Z/kZ).

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci