We show that the rank r component of the free idempotent generated semigroup
of the biordered set of the full linear monoid of n x n matrices over a
division ring Q has maximal subgroup isomorphic to the general linear group
GL_r(Q), where n and r are positive integers with r < n/3.Comment: 37 pages; Transactions of the American Mathematical Society (to
  appear). arXiv admin note: text overlap with arXiv:1009.5683 by other author

Dolinka, Igor

Gray, Robert

English

arXiv

We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal subgroup isomorphic to the general linear group $ GL_r(Q)$, where $ n$ and $ r$ are positive integers with $ r < n/3$

Gray, Robert D.

University of East Anglia digital repository

Maximal subgroups of free idempotent generated semigroups over the full linear monoid

We show that the rank 

  
    r
    r
  

 component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of 

  
    
      n
      ×
      n
    
    n \times n
  

 matrices over a division ring 

  
    Q
    Q
  

 has maximal subgroup isomorphic to the general linear group 

  
    
      G
      
        L
        r
      
      (
      Q
      )
    
    GL_r(Q)
  

, where 

  
    n
    n
  

 and 

  
    r
    r
  

 are positive integers with 

  
    
      r
      &gt;
      n
      
        /
      
      3
    
    r &gt; n/3
  

.</p

Igor Dolinka

Robert Gray

Crossref

Transactions of the American Mathematical Society

Maximal subgroups of free idempotent generated semigroups over the full
  linear monoid

Maximal subgroups of free idempotent generated semigroups over the full linear monoid

Abstract

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University of East Anglia digital repository

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