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
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页码：1 / 17
页数：17
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