On the Unitriangular Groups over Rational Numbers Field

被引：0

作者：

Gao, Rui ^{[1
]}

Liao, Jun ^{[1
]}

Liu, He Guo ^{[1
]}

Xu, Xing Zhong ^{[1
]}

机构：

[1] Hubei Univ, Sch Math & Stat, Wuhan 430062, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2022年 / 38卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Nilpotent groups; unitriangular groups; central series;

D O I：

10.1007/s10114-022-0485-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let U(n, DOUBLE-STRUCK CAPITAL Q) be the group of all n x n (upper) unitriangular matrices over rational numbers field DOUBLE-STRUCK CAPITAL Q. Let S be a subset of U(n, DOUBLE-STRUCK CAPITAL Q). In this paper, we prove that S is a subgroup of U(n, DOUBLE-STRUCK CAPITAL Q) if and only if the (i, j)-th entry S-ij satisfies some condition (see Theorem 3.5). Furthermore, we compute the upper central series and the lower central series for S, and obtain the condition that the upper central series and the lower central series of S coincide.

引用

页码：718 / 734

页数：17

共 18 条

[1] On the Unitriangular Groups over Rational Numbers Field
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Acta Mathematica Sinica, English Series, 2022, 38 : 718 - 734
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