Positively finitely related profinite groups
Positively finitely related profinite groups
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正有限相关有限群
DOI：
10.1007/s11856-018-1676-2
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发表时间：
2016
影响因子：
1
通讯作者：
Matteo Vannacci
中科院分区：
文献类型：
--
作者：
Steffen Kionke;Matteo Vannacci
我们定义并研究正有限相关（PFR）有限群的类别。正有限相关性是有限群的概率性质，它为定义有限群的更高有限性性质提供了第一步，该有限群概括了 Avinoam Mann 引入的正有限生成群。我们证明了 PFR 群的许多渐近特征，例如我们展示了以下内容：一个有限呈现的有限群是 PFR 当且仅当它在有限域上均匀地具有至多指数表示增长（换句话说：完整的群代数具有多项式最大理想增长）。从这些特征中，我们推断出 PFR 有限群的几个结构结果。
We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a first step to defining higher finiteness properties of profinite groups which generalize the positively finitely generated groups introduced by Avinoam Mann. We prove many asymptotic characterisations of PFR groups, for instance we show the following: a finitely presented profinite group is PFR if and only if it has at most exponential representation growth, uniformly over finite fields (in other words: the completed group algebra has polynomial maximal ideal growth). From these characterisations we deduce several structural results on PFR profinite groups.
紧p进解析群和算术群的表示zeta函数
影响因子：
2.5
作者：
Avni N
通讯作者：
Avni N