Algebra and Topology Seminar

4pm Tuesday 7 December 2004
Carlo Casolo
University of Florence

A characterization of semi-linear groups and an application

Given an elementary abelian p-group M, we may think of it as the additive group of a finite field. Then, by the semi-linear group on M, I mean the extension of the group of multiplications (in the field) by the Galois group. In the talk I will give a characterization (of certain subgroups) of semi-linear groups in terms of their point stabilizers, followed by some applications. For example: if the finite group G admits an irreducible complex representation whose dimension is divided by the product pq of two distinct prime numbers, then there exists a conjugacy class of G whose length is divided by pq.




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