Calculating Clifford classes for characters containing a linear character once

摘要

Given a finite group G, a normal subgroup N of G and an irreducible character chi of G, the Clifford class of X describes the Clifford theory including Schur indices of chi with respect to the normal subgroup N. Assume there is a subgroup U of N and a linear character theta of U with multiplicity 1 in the restriction of chi to U. We describe a method to calculate the Clifford class of chi in certain cases. This method helps, in particular, in the calculation of the Schur indices of the irreducible characters of the groups contained between the general linear and the special linear groups. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 7]