The classification of the simple periodic linear groups

1983 ◽  
Vol 41 (2) ◽  
pp. 103-116 ◽  
Author(s):  
Simon Thomas
Keyword(s):  
Linear Groups ◽  
Periodic Linear

scholarly journals THE -GENERATION OF THE SPECIAL LINEAR GROUPS OVER FINITE FIELDS

2016 ◽  
Vol 95 (1) ◽  
pp. 48-53 ◽  
Author(s):  
MARCO ANTONIO PELLEGRINI
Keyword(s):  
Finite Fields ◽  
Simple Groups ◽  
Linear Groups ◽  
Finite Simple Groups ◽  
Special Linear ◽  
Special Linear Groups

We complete the classification of the finite special linear groups $\text{SL}_{n}(q)$ which are $(2,3)$-generated, that is, which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple groups $\text{PSL}_{n}(q)$ which are $(2,3)$-generated.

scholarly journals Extensions of Periodic Linear Groups with Finite Unipotent Radical

2003 ◽  
Vol 31 (2) ◽  
pp. 959-968
Author(s):  
Richard E. Phillips† ◽  
Julianne G. Rainbolt ◽  
Jonathan I. Hall ◽  
Ulrich Meierfrankenfeld
Keyword(s):  
Unipotent Radical ◽  
Linear Groups ◽  
Periodic Linear

Periodic Linear Groups

1973 ◽  
pp. 112-133 ◽  
Author(s):  
Bertram A. F. Wehrfritz
Keyword(s):  
Linear Groups ◽  
Periodic Linear

scholarly journals Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence

2010 ◽  
Vol 146 (5) ◽  
pp. 1115-1164 ◽  
Author(s):  
A. I. Badulescu ◽  
D. Renard
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Multiplicity One ◽  
Unitary Dual ◽  
Strong Multiplicity ◽  
Local Results

AbstractIn a paper by Badulescu [Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations, Invent. Math. 172 (2008), 383–438], results on the global Jacquet–Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field were established, under the assumption that the local inner forms are split at archimedean places. In this paper, we extend the main local results of that article to archimedean places so that the above condition can be removed. Along the way, we collect several results about the unitary dual of general linear groups over ℝ, ℂ or ℍ which are of independent interest.

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