On the groups associated with a tropical n x n matrix

被引：1

作者：

Deng, Weina ^{[1
,2
]}

Zhao, Xianzhong ^{[1
]}

Cheng, Yanliang ^{[1
]}

Yu, Baomin ^{[3
]}

机构：

[1] Northwest Univ, Sch Math, Xian 710127, Shaanxi, Peoples R China

[2] Huanghuai Univ, Sch Math & Stat, Zhumadian 463000, Henan, Peoples R China

[3] Weinan Normal Univ, Sch Math & Stat, Weinan 714099, Shaanxi, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 639卷

基金：

中国国家自然科学基金;

关键词：

Tropical semiring; Tropical matrix; Permutation group; Idempotent normal matrix; Strongly regular matrix;

D O I：

10.1016/j.laa.2021.12.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

& nbsp;In this paper, the generalized centralizer group U-n(A) of a tropical n x n matrix A and the centralizer group P-n(E) of a tropical idempotent normal matrix E are introduced and studied. It is proved that U(n()A) is a product of two specific normal subgroups. And a structural description of P-n(E) is given when E is not strongly regular. It is also made some observations on E when P-n(E) is isomorphic to a 2-closed transitive permutation group on {1, 2, ... , n}. (C)& nbsp;2021 Elsevier Inc. All rights reserved.

引用

页码：1 / 17

页数：17

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