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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク List of transitive finite linear groups ： ウィキペディア英語版 List of transitive finite linear groups In mathematics, especially in areas of abstract algebra and finite geometry, the list of transitive finite linear groups is an important classification of certain highly symmetric actions of finite groups on vector spaces. The solvable finite 2-transitive groups were classified by Bertram Huppert. The classification of finite simple groups made possible the complete classification of finite doubly transitive permutation groups. This is a result by Christoph Hering. A finite 2-transitive group has a socle that is either a vector space over a finite field or a non-abelian primitive simple group; groups of the latter kind are almost simple groups and described elsewhere. This article provides a complete list of the finite 2-transitive groups whose socle is elementary abelian. Let $p$ be a prime, and $G$ a subgroup of the general linear group $GL(d,p)$ acting transitively on the nonzero vectors of the ''d''-dimensional vector space $(F\_p)^d$ over the finite field$F\_p$ with ''p'' elements. == Infinite classes == There are four infinite classes of finite transitive linear groups. * $G\; \backslash leq\; \backslash Gammap^d=q^;$ * $G\; \backslash triangleright\; G\_2(q)\text{'},\backslash \; p^d=q^6\backslash textp=2.$ Notice that the exceptional group of Lie type ''G''2(''q'') is usually constructed as the automorphism groups of the split octonions. Hence, it has a natural representation as a subgroup of the 7-dimensional orthogonal group O(7, ''q''). If ''q'' is even, then the underlying quadratic form polarizes to a degenerate symplectic form. Factoring out with the radical, one obtains an isomorphism between O(7, ''q'') and the symplectic group Sp(6, ''q''). The subgroup of Sp(6, ''q'') which corresponds to ''G''2(''q'')′ is transitive. In fact, for ''q''>2, the group ''G''2(''q'') = ''G''2(''q'')′ is simple. If ''q''=2 then ''G''2(2)′ ≅ PSU(3,3) is simple with index 2 in ''G''2(2). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of transitive finite linear groups」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.