Services on Demand
Journal
Article
Indicators
Cited by SciELO
Access statistics
Related links
Cited by Google
Similars in SciELO
Similars in Google
Share
Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Abstract
PRINS, Abraham Love. On the Fischer matrices of a group of shape 2 1+2n +:G. Rev.colomb.mat. [online]. 2022, vol.56, n.2, pp.189-211. Epub Feb 06, 2024. ISSN 0034-7426. https://doi.org/10.15446/recolma.v56n2.108379.
In this paper, the Fischer matrices of the maximal subgroup G = 21+8 +: (U 4(2):2) of U 6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8 +) ( 28: (U 4(2):2), where Z(21+8 +) denotes the center of the extra-special 2-group 21+8 +. Using this approach, the Fischer matrices and associated ordinary character table of G are computed in an elegantly simple manner. This approach can be used to compute the ordinary character table of any split extension group of the form 2 1+2n +: G, n ∈ N, provided the ordinary irreducible characters of 2 1+2n + extend to ordinary irreducible characters of its inertia subgroups in 2 1+2n +:G and also that the Fischer matrices M(g i ) of the quotient group 2 1+2n +: G/Z(2 1+2n +) ( 2 2n: G are known for each class representative g i in G.
Keywords : split extension; extra-special p-group; irreducible projective characters; Schur multiplier; inertia factor groups; Fischer matrices.