n*n非负整数矩阵的极大子群

doi:10.13371/j.cnki.chin.q.j.m.2020.02.006

数学季刊 ›› 2020, Vol. 35 ›› Issue (2): 186-193.doi: 10.13371/j.cnki.chin.q.j.m.2020.02.006

n*n非负整数矩阵的极大子群

收稿日期:2018-10-13 出版日期:2020-06-30 发布日期:2020-09-03

The Maximal Subgroups of n * n Nonnegative Integral Matrices

1. Lanzhou University of Technology, School of Science, Lanzhou 730050, China; 2. Northwest University, School of Mathematics, Xi'an 710127, China

Received:2018-10-13 Online:2020-06-30 Published:2020-09-03
About author:YANG Lin(1986-), female, native of Xianyang, Shaanxi, a lecturer of Lanzhou University of Technology, engages in algebra; REN Miao-miao(1986-), male, native of Yulin, Shaanxi, a associate professor of Northwest University, engages in algebra.
Supported by:
Supported by National Natural Science Foundation of China(11861045, 11701449)

摘要/Abstract

Abstract: In this paper we study the subgroup structure of the semigroup Mn(Z+) of all n * n nonnegative integral matrices under multiplication. We prove that every maximal subgroup of Mn(Z+) containing an idempotent element of rank r is isormorphic to Sr.

Key words: Green's relations, Basis submatrix, Maximal subgroup

中图分类号:

杨琳, 任苗苗. n*n非负整数矩阵的极大子群[J]. 数学季刊, 2020, 35(2): 186-193.

YANG Lin, REN Miao-miao. The Maximal Subgroups of n * n Nonnegative Integral Matrices[J]. Chinese Quarterly Journal of Mathematics, 2020, 35(2): 186-193.

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n*n非负整数矩阵的极大子群

The Maximal Subgroups of n * n Nonnegative Integral Matrices

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