Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutation representations of nonsplit extensions involving alternating
  groups   L. Babai has shown that a faithful permutation representation of a nonsplit
extension of a group by an alternating group $A_k$ must have degree at least
$k^2(\frac{1}{2}-o(1))$, and has asked how sharp this lower bound is. We prove
that Babai's bound is sharp (up to a constant factor), by showing that there
are such nonsplit extensions that have faithful permutation representations of
degree $\frac{3}{2}k(k-1)$. We also reprove Babai's quadratic lower bound with
the constant $\frac{1}{2}$ improved to 1 (by completely different methods).

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol