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In the area of modern algebra known as group theory, the Tits group 2''F''4(2)′ () is a finite simple group of order : 211 · 33 · 52 · 13 = 17971200 : ≈ 2. It is sometimes considered a 27th sporadic group. ==History and properties== The Ree groups 2''F''4(22''n''+1) were constructed by , who showed that they are simple if ''n'' ≥ 1. The first member of this series 2''F''4(2) is not simple. It was studied by who showed that it is almost simple, its derived subgroup 2''F''4(2)′ of index 2 being a new simple group, now called the Tits group. The group 2''F''4(2) is a group of Lie type and has a BN pair, but the Tits group itself does not have a BN pair. Because the Tits group is not strictly a group of Lie type, it is sometimes regarded as a 27th sporadic group.〔For instance, by the ATLAS of Finite Groups and its (web-based descendant )〕 The Schur multiplier of the Tits group is trivial and its outer automorphism group has order 2, with the full automorphism group being the group 2''F''4(2). The Tits group occurs as a maximal subgroup of the Fischer group Fi22. The groups 2''F''4(2) also occurs as a maximal subgroup of the Rudvalis group, as the point stabilizer of the rank-3 permutation action on 4060 = 1 + 1755 + 2304 points. The Tits group is one of the simple N-groups, and was overlooked in John G. Thompson's first announcement of the classification of simple ''N''-groups, as it had not been discovered at the time. It is also one of the thin finite groups. The Tits group was characterized in various ways by and . 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「Tits group」の詳細全文を読む スポンサード リンク
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