论文标题
自动实现Hopf Galois结构
Automatic realization of Hopf Galois structures
论文作者
论文摘要
我们考虑在可分开的场扩展上的Hopf Galois结构$ p^n $的$ l/k $，对于$ p $ a奇数，$ n \ geq 3 $。对于$ p> n $，我们证明$ l/k $最多具有一种Abelian类型的Hopf Galois结构。 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 $。
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 $1\leq m \leq n$.
