Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphism group of the complete transposition graph   The complete transposition graph is defined to be the graph whose vertices
are the elements of the symmetric group $S_n$, and two vertices $\alpha$ and
$\beta$ are adjacent in this graph iff there is some transposition $(i,j)$ such
that $\alpha=(i,j) \beta$. Thus, the complete transposition graph is the Cayley
graph $\Cay(S_n,S)$ of the symmetric group generated by the set $S$ of all
transpositions. An open problem in the literature is to determine which Cayley
graphs are normal. It was shown recently that the Cayley graph generated by 4
cyclically adjacent transpositions is not normal. In the present paper, it is
proved that the complete transposition graph is not a normal Cayley graph, for
all $n \ge 3$. Furthermore, the automorphism group of the complete
transposition graph is shown to equal \[ \Aut(\Cay(S_n,S)) = (R(S_n) \rtimes
\Inn(S_n)) \rtimes \mathbb{Z}_2, \] where $R(S_n)$ is the right regular
representation of $S_n$, $\Inn(S_n)$ is the group of inner automorphisms of
$S_n$, and $\mathbb{Z}_2 = \langle h \rangle$, where $h$ is the map $\alpha
\mapsto \alpha^{-1}$.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th