The pro-supersolvable topology on a free group: Deciding denseness
The pro-supersolvable topology on a free group: Deciding denseness
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自由群上的超可解拓扑：决定密度
DOI：
10.1016/j.jalgebra.2024.02.002
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发表时间：
2024
影响因子：
0.9
通讯作者：
Marion C
中科院分区：
文献类型：
--
作者：
Marion C
设F是任意秩的自由群，H是F的一个n-生成子群.给定有限群的伪簇V，即一类有限群在取子群、直积和有限直积下闭，我们赋予F以pro-V拓扑。我们的主要结果是：H是否pro-Su稠密是可判定的，这里Su ∈ S分别表示所有有限超可解群和所有有限可解群的伪簇.我们的动机源于以下开放的问题：它是决定是否H是亲S密集？
Let F be a free group of arbitrary rank and let H be a finitely generated subgroup of F. Given a pseudovariety V of finite groups, ie a class of finite groups closed under taking subgroups, quotients and finitary direct products, we endow F with its pro-V topology. Our main result states that it is decidable whether H is pro-Su dense, where Su⊂ S denote respectively the pseudovarieties of all finite supersolvable groups and all finite solvable groups. Our motivation stems from the following open problem: is it decidable whether H is pro-S dense?