Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proportions of elements with given 2-part order in finite classical
  groups of odd characteristic   For an element $g$ in a group $X$, we say that $g$ has 2-part order $2^{a}$
if $2^{a}$ is the largest power of 2 dividing the order of $g$. We prove lower
bounds on the proportion of elements in finite classical groups in odd
characteristic that have certain 2-part orders. In particular, we show that the
proportion of odd order elements in the symplectic and orthogonal groups is at
least $C/\ell^{3/4}$, where $\ell$ is the Lie rank, and $C$ is an explicit
constant. We also prove positive constant lower bounds for the proportion of
elements of certain 2-part orders independent of the Lie rank. Furthermore, we
describe how these results can be used to analyze part of Yal\c{c}inkaya's
Black Box recognition algorithm for finite classical groups in odd
characteristic.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas