嵌套GVZ-群的中心列刻画
Characterizations of nested GVZ-groups by central series
摘要：
群的许多性质都可以通过特定正规列的存在性来定义。经典的例子是可解性、超可解性和零解性。在幂零群群中有一种叫做嵌套GVZ群的群，在这种群中，不可约特征标的中心形成一个链，并且每个不可约特征标从其中心消失。本文证明了套GVZ-群可以用某个升中心列的存在性或某个降中心列的存在性来刻画。
英文摘要：
Many properties of groups can be defined by the existence of a particular normal series. The classic examples being solvability, supersolvability and nilpotence. Among the nilpotent groups are the so-called nested GVZ-groups --- groups where the centers of the irreducible characters form a chain, and where every irreducible character vanishes off of its center. In this paper, we show that nested GVZ-groups can be characterized by the existence of a certain ascending central series, or by the existence of a certain descending central series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
