The Maximal Subgroups of n * n Nonnegative Integral Matrices

YANG Lin, REN Miao-miao

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

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 2: 186 - 193

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.02.006

The Maximal Subgroups of n * n Nonnegative Integral Matrices

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

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.

Received date: 2018-10-13

Online published: 2020-09-03

Supported by

Supported by National Natural Science Foundation of China(11861045, 11701449)

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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

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

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