Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-Parts of real class sizes   We investigate the structure of finite groups whose non-central real class
sizes have the same $2$-part. In particular, we prove that such groups are
solvable and have $2$-length one. As a consequence, we show that a finite group
is solvable if it has two real class sizes. This confirms a conjecture due to
G. Navarro, L. Sanus and P. Tiep.

5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin