The Unipotency Of Eleventh Order Matrix Group With No More Than Seven Jordan Blocks

At present,the classification of finite simple groups has been perfectly solved.Group theory will have the tendency to develop towards infinite groups.Therefore,finitely generated infinite groups are an intermediate bridge.It is more general to explore the most basic and concise tools.Therefore,this topic only uses linear representation and the product and combination properties of primitive elements to study binary generated free groups.This is a meaningful exploration.Any group must be a homomorphic image of a free group.The automorphism group of a free group often shows that the primitive elements are unipotent.The most basic of finitely generated free groups is binary generated free groups.Therefore,this topic chooses to study the determination of groups whose primitive elements in the linear representation image of binary generated free groups are unipotent.It is of great significance for binary generated free groups and finitely generated free groups.There have been two trends in the determination of unipotence.In this paper,the decision is made when the dimension is selected as a specific value.The research method is gradually extended from low dimension to high dimension.Another way of thinking is to classify all the representation dimensions uniformly,and each class covers any fixed representation dimension.According to the existing conclusions,the case that the dimension is not higher than ten is basically solved.The dimension is eleven,and the maximum Jordan block contained in primitive elements is greater than seven.Therefore,this paper studies the unipotence of the matrix group of the eleventh order with the largest Jordan block of primitive elements not greater than seven.The focus is on the case where the standard types of a primitive are diag（J₇,J₄）,diag（J₇,J₂,J₂）and diag（J₆,E₅）.It is pointed out that in these cases,when the primitive element is unipotent,matrix groups generated by two variables are also unipotent groups...