scholarly journals Generic central extensions and projective representations of finite groups

2001 ◽  
Vol 5 (6) ◽  
pp. 129-146 ◽  
Author(s):  
Rachel Quinlan
Keyword(s):  
Finite Groups ◽  
Central Extensions ◽  
Representations Of Finite Groups ◽  
Projective Representations

Rational projective representations of finite groups

1979 ◽  
Vol 86 (3) ◽  
pp. 413-419 ◽  
Author(s):  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Representation ◽  
Rational Numbers ◽  
Linear Character ◽  
Cyclic Subgroups ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
Image Position

Let G bea finite group, let C1, …, Cn be the cyclic subgroups of G and let 1i be the identity linear character of Ci (1 ≤ i ≤ n). It is a well-known result of Artin ((l), 39·1) that a character x of a linear representation of G over the rational numbers may be writtenwhere a1, …, an are integers. In this note, we establish an analogue of this result for characters of projective representations over the rational numbers.

scholarly journals On tensor factorisation for representations of finite groups

2004 ◽  
Vol 69 (1) ◽  
pp. 161-171 ◽  
Author(s):  
Emanuele Pacifici
Keyword(s):  
Finite Group ◽  
Tensor Product ◽  
Finite Groups ◽  
Group Structure ◽  
Complex Representation ◽  
Normal Subgroups ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.

Real projective representations of finite groups

1990 ◽  
Vol 107 (1) ◽  
pp. 27-32 ◽  
Author(s):  
P. N. Hoffmann ◽  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Schur Multiplier ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

The projective representations of a finite group G over a field K are divided into sets, each parametrized by an element of the group H2(G, Kx). The latter is the Schur multiplier M(G) when K = ℂ.

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