Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite $p$-groups whose central automorphisms are all class
  preserving   We obtain certain results on a finite $p$-group whose central automorphisms
are all class preserving. In particular, we prove that if $G$ is a finite
$p$-group whose central automorphisms are all class preserving, then $d(G)$ is
even, where $d(G)$ denotes the number of elements in any minimal generating set
for $G$. As an application of these results, we obtain some results regarding
finite $p$-groups whose automorphisms are all class preserving. In particular,
we prove that if $G$ is a finite $p$-groups whose automorphisms are all class
preserving, then order of $G$ is at least $p^8$ and the order of the
automorphism group of $G$ is at least $p^12$.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc