Open AccessThe Unipotent Condition of Linear Groups Generated by Matrices with Primitive Elements Jorden Blocks of Orders no More Than Eight
Author(s) -
Xiaoguang Yang,
Guosheng Pan
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/790/1/012073
Subject(s) - unipotent , logarithm , mathematics , group (periodic table) , matrix (chemical analysis) , pure mathematics , algebra over a field , combinatorics , mathematical analysis , chemistry , chromatography , organic chemistry
In this paper, the combinatorial properties of free group generators are studied with help of calculation tool, matrix logarithm, and Jacobson radical. The unipotency of matrix groups can be better delineated by these new combinatorial properties, and a new necessary and sufficient unipotent condition of matrix group whose primitive elements Jordan blocks have orders no more than eight, as well as of free groups, will be given. Our result improves the relative theories.