Counting irreducible modules for profinite groups
Counting irreducible modules for profinite groups
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计算有限群的不可约模
DOI：
10.4171/rmi/1382
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Matteo Vannacci
中科院分区：
文献类型：
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作者：
Ged Corob Cook;Steffen Kionke;Matteo Vannacci
本文主要研究有限域上有限群的表示增长。研究了具有一致有界指数表示增长（UBERG）的群的结构。利用基于冠的幂，我们得到了群具有UBERG的一些充分必要条件。作为应用，我们证明了UBERG群类在分裂扩张下是闭的，但在一般扩张下不是闭的。另一方面，我们表明，密切相关的概率有限性属性$PFP_1$是封闭的扩展。此外，我们还证明了具有UBERG的FP_1型profinite群总是可生成的，并且证明了UBERG是pro-nilpotent群类中的pro-nilpotent群。利用有限群的无穷乘积，我们构造了几个具有意想不到性质的前有限群的例子：（1）一个不可能是超指数生成的UBERG群，（2）一个$PFP_\infty$型群，它不是UBERG群也不是超指数生成的，（3）一个具有超指数子群增长的$PFP_\infty$型群.
This article is concerned with the representation growth of profinite groups over finite fields. We investigate the structure of groups with uniformly bounded exponential representation growth (UBERG). Using crown-based powers we obtain some necessary and some sufficient conditions for groups to have UBERG. As an application we prove that the class of UBERG groups is closed under split extensions but fails to be closed under extensions in general. On the other hand, we show that the closely related probabilistic finiteness property $PFP_1$ is closed under extensions. In addition, we prove that profinite groups of type $FP_1$ with UBERG are always finitely generated and we characterise UBERG in the class of pro-nilpotent groups. Using infinite products of finite groups, we construct several examples of profinite groups with unexpected properties: (1) an UBERG group which cannot be finitely generated, (2) a group of type $PFP_\infty$ which is not UBERG and not finitely generated and (3) a group of type $PFP_\infty$ with superexponential subgroup growth.
影响因子：
1
作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
通讯作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
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