Minimal permutation representations of finite simple orthogonal groups

Primitive parabolic permutation representations for finite simple orthogonal groups in odd dimensions

“…Zq−1 2 of index 2 in GL k (q) for l − 2k = 1, and to a subgroup (SL k (q). Zq−1 2 × Ω l−2k (q)). Z 2 for l − 2k > 1.…”

“…If dim W = 1 then a permutation representation of a group G on Γ has minimal degree (see [2] for details).…”

“…By now these parameters have been obtained for minimal faithful permutation representations of all finite simple groups of Lie type (see [1][2][3][4][5][6]). An important class of permutation representations for finite groups of Lie type is formed by parabolic representations, that is, representations on cosets with respect to parabolic subgroups.…”

The ranks of primitive parabolic permutation representations of the simple groups B l (q), C l (q), and D l (q)

“…It is important to note the completion in [6][7][8][9][10][11][12][13] of the classification of the minimal degree faithful permutation representations for finite simple groups of Lie type.…”

Grupos finitos e quebra de simetria no código genético

“…Se Gé um grupo finito simples há informações detalhadas sobre a "menor" representação permutacional fiel de G [114,115,148,149,150,151], que podem ser usadas para construí-la. Já para extensões ascendentes e descendentes de um grupo finito simples G só e possível obter algumas informações qualitativas [14,15,103].…”