Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the probability distribution associated to commutator word map in
  finite groups \rom{2}   Let $P(G)$ denotes the set of sizes of fibers of non-trivial commutators of
the commutator word map. Here, we prove that $|P(G)|=1$, for any finite group
$G$ of nilpotency class $3$ with exactlly two conjugacy class sizes. We also
show that for given $n\geq 1$, there exists a finite group $G$ of nilpotency
class $2$ with exactlly two conjugacy class sizes such that $|P(G)|=n$.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn