Local Representation Theory and Simple Groups

10.4171/185 ◽  
2018 ◽  
Keyword(s):  
Representation Theory ◽  
Simple Groups ◽  
Local Representation

scholarly journals On the Modular Version of Ito’s Theorem on Character Degrees for Groups of Odd Order

1987 ◽  
Vol 105 ◽  
pp. 109-119 ◽  
Author(s):  
Olaf Manz
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Prime Number ◽  
Character Degrees ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Classical Representation ◽  
Odd Order ◽  
Complex Characters

One of the most useful theorems in classical representation theory is a result due to N. Ito, which can be stated using the classification of the finite simple groups in the following way.THEOREM (N. Ito, G. Michler). Let Irr (G) be the set of all irreducible complex characters of the finite group G and q be a prime number. Then if and only if G has a normal, abelian Sylow-q-subgroup.

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