Calculating Clifford classes for characters containing a linear character once.
Because of the details, spread out over the paper, the contents of the paper is difficult to expose in a short review. Let us confine ourselves to the following remarks. In previous papers, the author wrote about equivalence of \(G\)-classes [see J. Pure Appl. Algebra 98, No. 2, 209-222 (1995; Zbl 0833.20012) and Commun. Algebra 22, No. 12, 5037-5078 (1994; Zbl 0810.20008) and Proc. Am. Math. Soc. 123, No. 6, 1655-1660 (1995; Zbl 0841.20013)], on Clifford theory for cyclic quotient groups [J. Algebra 227, No. 1, 133-158 (2000; Zbl 0959.20010)] and on a formula for calculating some Schur indices [J. Algebra 227, No. 1, 124-132 (2000; Zbl 0976.20009)]. Here, he pursues these matters further. To be specific about the paper under review: Given a finite group \(G\), a normal subgroup \(N\) of \(G\) and \(\chi\in\text{Irr}(G)\), the Clifford class of \(\chi\) describes the Clifford theory including Schur indices of \(\chi\) with respect to \(N\). Assume there exists a subgroup \(U\) of \(N\) and a linear character \(\vartheta\) of \(U\) with \((\chi_N,\vartheta)=1\). Here, a method is described to calculate the Clifford class of \(\chi\) in certain cases. This method helps, for instance, in the calculation of the Schur indices of the irreducible characters of the groups contained between the general linear groups and the special linear groups.
scientific article; zbMATH DE number 1867980