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摘要翻译：
给出了有限群半自由的条件，半自由比自由更一般，半自由比拟自由更有限制。特别地，每个射影半自由的profliment群都是自由的。我们证明了自由群通常的持久性质可以延续到半自由群。利用这一点，我们得出结论：如果k是一个分离闭域，那么k((x，y))的许多域扩张都有自由绝对Galois群。
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英文标题：
《Permanence criteria for semi-free profinite groups》
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作者：
Lior Bary-Soroker, Dan Haran, David Harbater
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Group Theory 群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We introduce the condition of a profinite group being semi-free, which is more general than being free and more restrictive than being quasi-free. In particular, every projective semi-free profinite group is free. We prove that the usual permanence properties of free groups carry over to semi-free groups. Using this, we conclude that if k is a separably closed field, then many field extensions of k((x,y)) have free absolute Galois groups.
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PDF链接：
https://arxiv.org/pdf/0810.0845
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