Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nilpotent groups and conjugacy classes   Let $G$ be a nilpotent group and $a\in G$. Let $a^G=\{g^{-1}ag\mid g\in G\}$
be the conjugacy class of $a$ in $G$. Assume that $a^G$ and $b^G$ are conjugacy
classes of $G$ with the property that $|a^G|=|b^G|=p$, where $p$ is an odd
prime number.
  Set $a^G b^G=\{xy\mid x\in a^G, y\in b^G\}$. Then either $a^G b^G=(ab)^G$ or
$a^G b^G$ is the union of at least $\frac{p+1}{2}$ distinct conjugacy classes.
As an application of the previous result, given any nilpotent group $G$ and any
conjugacy class $a^G$ of size $p$, we describe the square $a^G a^G$ of $a^G$ in
terms of conjugacy classes of $G$.

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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph