Teorema di Alperin–Brauer–Gorenstein
In matematica, 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
{stile di visualizzazione M_{11}}
. Alperin, Brauer & Gorenstein (1970) proved this in the course of 261 pagine. The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, cap. 7), and presented in some detail in Kwon et al. (1980).
Teorema di Alperin–Brauer–Gorenstein
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In matematica, il Teorema di Alperin–Brauer–Gorenstein characterizes the finite simple groups insieme a quasidihedral or wreathed[1] Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups o 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 pagine.
The subdivision by 2-fusion is sketched there, given as an exercise in Gorenstein (1968, cap. 7), and presented in some detail in Kwon et al. (1980).
Appunti[]
- ^ A 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a prodotto diretto of two cyclic groups of the same order, questo è, if it is the wreath product of a cyclic 2-group with the symmetric group Su 2 punti.
Riferimenti[]
Alperin, J. l.Brauer, R.Gorenstein, D. (1970), "Finite groups with quasi-dihedral and wreathed Sylow 2-subgroups.", Transazioni dell'American Mathematical Society, Società matematica americana, 151 (1): 1–261, doi:10.2307/1995627, ISSN 0002-9947, JSTOR 1995627, SIG 0284499
- Gorenstein, D. (1968), Finite groups, Harper & Row Publishers, SIG 0231903
- Kwon, T.; Lee, K.; Cho, IO.; Park, S. (1980), "On finite groups with quasidihedral Sylow 2-groups", Journal of the Korean Mathematical Society, 17 (1): 91–97, ISSN 0304-9914, SIG 0593804, archived from the original Su 2011-07-22, recuperato 2010-07-16
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