Théorème d'Alperin – Brauer – Gorenstein
En mathématiques, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathed[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group
{style d'affichage M_{11}}
. Alperin, Brauer & Gorenstein (1970) proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, Ch. 7), and presented in some detail in Kwon et al. (1980).
Théorème d'Alperin – Brauer – Gorenstein
Aller à la navigation
Aller à la recherche
Dans mathématiques, la Théorème d'Alperin – Brauer – Gorenstein characterizes the finite simple groups avec quasidihedral or wreathed[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups ou projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group
!["M_{11}"]("https://wikimedia.org/api/rest_v1/media/math/render/svg/83f4effa72a74f4d82e6122f986c61c7a4a12318")
Alperin, Brauer & Gorenstein (1970) proved this in the course of 261 pages.
The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, Ch. 7), and presented in some detail in Kwon et al. (1980).
Remarques[]
- ^ A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a produit direct of two cyclic groups of the same order, C'est, if it is the wreath product of a cyclic 2-group with the symmetric group sur 2 points.
Références[]
Alperin, J. L.Brauer, R.Gorenstein, ré. (1970), "Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.", Transactions de l'American Mathematical Society, Société mathématique américaine, 151 (1): 1–261, est ce que je:10.2307/1995627, ISSN 0002-9947, JSTOR 1995627, M 0284499
- Gorenstein, ré. (1968), Finite groups, harpiste & Row Publishers, M 0231903
- Kwon, T; Lee, K; Cho, JE.; Park, S. (1980), "On finite groups with quasidihedral Sylow 2-groups", Journal of the Korean Mathematical Society, 17 (1): 91–97, ISSN 0304-9914, M 0593804, archived from the original sur 2011-07-22, récupéré 2010-07-16
!["Stub]("/wiki/File:Rubik%27s_cube_v3.svg") | Cette abstract algebra-related article is a stub. You can help Wikipedia by expanding it. |
Si vous voulez connaître d'autres articles similaires à Théorème d'Alperin – Brauer – Gorenstein vous pouvez visiter la catégorie Abstract algebra stubs.
Laisser un commentaire