论文标题
某些基本$ P $ -Abelian Extensions的Galois模块结构
Galois module structure of some elementary $p$-abelian extensions
论文作者
论文摘要
我们确定当$ \ text {gal}（k/f）$是任何有限的$ p $ - 组时，基本$ p $ p $ p $ p $ -p $ -p $ k $的参数化空间的GALOIS模块结构，假设是在最大$ $ $ f $ $ f $ $ $ $ $ $ $ $ $ $ $ pro的$ p $ $ p $ pro的$ p $ pro的最大$ p $的假设上unity的根，如果$ \ text {char}（f）\ neq p $。
We determine the Galois module structure of the parameterizing space of elementary $p$-abelian extensions of a field $K$ when $\text{Gal}(K/F)$ is any finite $p$-group, under the assumption that the maximal pro-$p$ quotient of the absolute Galois group of $F$ is a free, finitely generated pro-$p$ group, and that $F$ contains a primitive $p$th root of unity if $\text{char}(F) \neq p$.
