论文标题
马格努斯形成的同事和单词的组合
Cohomology and the Combinatorics of Words for Magnus Formations
论文作者
论文摘要
对于完全订购的$ x $ $ p $ $ p $和免费的pro-p $ g $ g $ $ x $，我们考虑封闭的正常子组$ g^φ$ $ g $的$ g $，这些$ g $由$ p $ $ p $ - 迭代的换向器的能力与Alphabet $ x $相关的lyndon单词相关的迭代换向器。我们以$ x $上的shuffle代数来表达$ h^2（g/g^φ）$组合。这部分扩展了较低$ p $中央和$ p $ zassenhaus滤过$ g $的现有结果。
For a prime number $p$ and a free pro-$p$ group $G$ on a totally ordered basis $X$, we consider closed normal subgroups $G^Φ$ of $G$ which are generated by $p$-powers of iterated commutators associated with Lyndon words in the alphabet $X$. We express the profinite cohomology group $H^2(G/G^Φ)$ combinatorically, in terms of the shuffle algebra on $X$. This partly extends existing results for the lower $p$-central and $p$-Zassenhaus filtrations of $G$.
