Construction of the Rudvalis group of order 145,926,144,000☆
Construction of the Rudvalis group of order 145,926,144,000☆
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Rudvalis集团建设工程订单145,926,144,000☆
DOI：
10.1016/0021-8693(73)90063-x
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
D.B Wales
中科院分区：
文献类型：
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作者：
J.H Conway;D.B Wales
最近，Arunas Rudvalis[1]提供了一个新的简单群R的存在证据，其阶为145,926,144,000= 2r4* 33* 5a。7 * 13。29. 他将这个群描述为4060个字母上的3阶置换群，其中一个点的稳定子是（非简单）Ree群F= V ',(2)，其轨道大小分别为1、1755、2304，对应于F的20480阶和15600阶的子群。其中第一个是F的对合的中心化子，而第二个有已知的P '的子群L= PSLa（25）作为指标2的子群（见参考文献[4]）。由于R中的一个对折没有不动点，所以只有2030个2周期，Griess和Schur[2]的论证表明R有一个适当的双盖2R。Rudvalis和Frame给出了证据，证明这个群有一个28维的复表示，不会在f上分裂（Feit和Lyons在r的进一步假设下证明了这一点）。在构造群的时候，我们假设这个2R的酉表示存在，但是独立于这个假设，我们得出结论，这个构造定义了一个群2R，它的中心商是r。结果证明，在217的2%维表示中，4060个字母变成了四个向量~ 1，iv,-ZJ，—iv的4060个四联体。任何四联体的稳定器都是（不适当的）双盖2F (F)和稳定器
Recently, Arunas Rudvalis [l] provided evidence for the existence of a new simple group R of order 145,926,144,000= 2r4* 33* 5a. 7* 13. 29. He describes the group as a rank 3 permutation group on 4060 letters, in which the stabilizer of a point is the (nonsimple) Ree group F= V’,(2), which has orbits of sizes 1, 1755, 2304, corresponding to subgroups of F of orders 20480 and 15600. The first of these is the centralizer of an involution of F, while the second has the known subgroup L= PSLa (25) of P’(see Ref.[4]) as a subgroup of index 2.Since one of the involutions in R has no fixed point and so just 2030 2-cycles, an argument of Griess and Schur [2] shows that R has a proper double cover 2R. Rudvalis and Frame gave evidence for supposing that this group had a 28-dimensional complex representation not splitting over F.(Feit and Lyons have proved this under further assumptions on R.) We suppose that this unitary representation of 2R exists while constructing the group, but then conclude independently of this supposition that the construction defines a group 2R whose central quotient is R. It turns out that in the 2% dimensional representation of 217 the 4060 letters become 4060 quadruplets of four vectors~ 1, iv,-ZJ,--iv. The stabilizer of any quadruplet is a (not proper) double cover 2F of F, and the stabilizer