Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the norm of the centralizers of a group   For any group G, let C(G) denote the intersection of the normal- izers of
centralizers of all elements of G. Set C0 = 1. Define Ci+1(G)=Ci(G) =
C(G=Ci(G)) for i ? 0. By C1(G) denote the terminal term of the ascending
series. In this paper, we show that a finitely generated group G is nilpotent
if and only if G = Cn(G) for some positive integer n.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg