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On faithful irreducible projective representations of finite groups over a field of characteristicp

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
321
Issue
1
Identifiers
DOI: 10.1016/j.jalgebra.2008.08.031
Keywords
  • Faithful Projective Representations
  • Faithful Representations
  • Modular Projective Representations
  • Modular Representations
  • Projective Representations
  • Twisted Group Algebras

Abstract

Abstract Let K be a field of finite characteristic p and G a finite group with a normal Sylow p-subgroup. We give necessary and sufficient conditions for G to have a faithful irreducible projective representation over K. In the case when G is an abelian p-group and K is not a perfect field we find also all dimensions of faithful irreducible projective representations of G over K and show that the group G has infinitely many isomorphism classes of faithful irreducible projective representations of each possible dimension d ≠ 1 .

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