Parabolic subgroups of $\mathrm{SL}_n$ and $\mathrm{Sp}_{2l}$ over a~Dedekind ring of arithmetic type
    
    
  
  
  
      
      
      
        
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 5-21
    
  
  
  
  
  
    
      
      
        
      
      
      
    Voir la notice de l'article provenant de la source Math-Net.Ru
            
              			Let $R$ be a commutative ring all of whose proper factor rings are finite and such that there exists a unit of infinite order. We show that for a subgroup $P$ in $G=\mathrm{SL}(n,R)$, $n\ge3$, or in $G=\mathrm{Sp}(2l,R)$, $l\ge2$, containing Borel subgroup $B$, the following alternative holds. Either $P$ contains a relative elementary subgroup $E_I$ for some ideal $I\neq0$, or $H$ is contained in a proper standard parabolic subgroup. For Dedekind rings of arithmetic type this allows, under some mild additional assumptions on units, to completely describe overgroups of $B$ in $G$. Bibl. – 30 titles.
			
            
            
            
          
        
      @article{ZNSL_2010_375_a0,
     author = {A. V. Alexandrov and N. A. Vavilov},
     title = {Parabolic subgroups of $\mathrm{SL}_n$ and $\mathrm{Sp}_{2l}$ over {a~Dedekind} ring of arithmetic type},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--21},
     publisher = {mathdoc},
     volume = {375},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a0/}
}
                      
                      
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                    %0 Journal Article
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%A N. A. Vavilov
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%J Zapiski Nauchnykh Seminarov POMI
%D 2010
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                    A. V. Alexandrov; N. A. Vavilov. Parabolic subgroups of $\mathrm{SL}_n$ and $\mathrm{Sp}_{2l}$ over a~Dedekind ring of arithmetic type. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 5-21. http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a0/