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On the Fischer matrices of a group of shape 21+2n + :G
Sobre las matrices de Fischer de un grupo de la forma 21+2n + :G
DOI:
https://doi.org/10.15446/recolma.v56n2.108379Palabras clave:
split extension, extra-special p-group, irreducible projective characters, Schur multiplier, inertia factor groups, Fischer matrices (en)extensión escindida, p-grupo extra especial, caracteres proyectivos irreducibles, multiplicador de Schur, inertia factor groups, matrices de Fischer (es)
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In this paper, the Fischer matrices of the maximal subgroup G = 21+8+ : (U4(2):2) of U6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8+) = 28 : (U4(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 21+2n+ :G, n ∈ N, provided the ordinary irreducible characters of 21+2n+ extend to ordinary irreducible characters of its inertia subgroups in 21+2n+:G and also that the Fischer matrices M(gi) of the quotient group 21+2n+ :G/Z(21+2n+) = 22n:G are known for each class representative gi in G.
En este artículo, las matrices de Fischer del subgrupo maximal G = 21+8+ : (U4(2):2) de U6(2):2 serán derivadas a partir de las matrices de Fischer del grupo cociente Q = G/Z(21+8+) = 28 : (U4(2):2), donde Z(21+8+) denota el centro del grupo 2-extra especial 21+8+. Usando este enfoque, las matrices de Fischer y la tabla de caracteres asociadas de G son calculados de una manera elegante y simple. Este enfoque se puede utilizar para calcular la tabla de caracteres de cualquier extensión escindida de la forma 21+2n+ :G, n ∈ N, siempre y cuando los caracteres irreducibles ordinarios de 21+2n+ se extiendan a caracteres irreducibles ordinarios de sus subgrupos de inercia en 21+2n+:G y también que las matrices de Fischer M(gi) del grupo cociente 21+2n+ :G/Z(21+2n+) = 22n:G sean conocidas para cada representante de clase gi en G.
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