Finite groups of OTP projective representation type

2012 ◽  
Vol 126 (1) ◽  
pp. 35-51
Author(s):  
Leonid F. Barannyk
Keyword(s):  
Finite Groups ◽  
Projective Representation ◽  
Representation Type

Godeaux–Serre varieties and the étale index

2013 ◽  
Vol 11 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Benjamin Antieau ◽  
Ben Williams
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Function Fields ◽  
Projective Representation ◽  
High Dimensional ◽  
Index Problem ◽  
Completion Theorem

AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.

Representation type of finite groups

1982 ◽  
Vol 20 (6) ◽  
pp. 2515-2528 ◽  
Author(s):  
V. M. Bondarenko ◽  
Yu. A. Drozd
Keyword(s):  
Finite Groups ◽  
Representation Type

Finite Linear Groups of Degree Six

1971 ◽  
Vol 23 (5) ◽  
pp. 771-790 ◽  
Author(s):  
J. H. Lindsey
Keyword(s):  
Tensor Product ◽  
Finite Groups ◽  
Existence And Uniqueness ◽  
Projective Representation ◽  
Linear Groups ◽  
3 Dimensional ◽  
Dimensional Group ◽  
Complex Linear ◽  
Finite Linear ◽  
Complex Number Field

In this paper we classify finite groups G with a faithful, quasiprimitive (see Notation), unimodular representation X with character χ of degree six over the complex number field. There are three gaps in the proof which are filled in by [16; 17]. These gaps concern existence and uniqueness of simple, projective, complex linear groups of order 604800, |LF(3, 4)|, and |PSL4(3)|. By [19], X is a tensor product of a 2-dimensional and a 3-dimensional group, or a subgroup thereof, or X corresponds to a projective representation of a simple group, possibly extended by some automorphisms. The tensor product case is discussed in section 10. Otherwise, we assume that G/Z(G) is simple. We discuss which automorphisms of G/Z(G) extend the representation X (that is, lift to the central extension G and fix the character corresponding to X) just after we find X(G).

Enumeration of Finite Groups

2007 ◽  
Author(s):  
Simon R. Blackburn ◽  
Peter M. Neumann ◽  
Geetha Venkataraman
Keyword(s):  
Finite Groups
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