Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic realization of Hopf Galois structures   We consider Hopf Galois structures on a separable field extension $L/K$ of
degree $p^n$, for $p$ an odd prime number, $n\geq 3$. For $p > n$, we prove
that $L/K$ has at most one abelian type of Hopf Galois structures. For a
nonabelian group $N$ of order $p^n$, with commutator subgroup of order $p$, we
prove that if $L/K$ has a Hopf Galois structure of type $N$, then it has a Hopf
Galois structure of type $A$, where $A$ is an abelian group of order $p^n$ and
having the same number of elements of order $p^m$ as $N$, for $1\leq m \leq n$.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin