A simple group of order 44,352,000
A simple group of order 44,352,000
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DOI：
10.1007/bf01110435
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发表时间：
1968-04
影响因子：
0.8
通讯作者：
D. G. Higman;C. Sims
中科院分区：
文献类型：
--
作者：
D. G. Higman;C. Sims
标题的群G被得到为100次的本原置换群，其中点的稳定子具有长度为1、22和77的轨道，并且与Mathieu群M22同构。因此，G在[1]的意义下具有3的排名。G是由Steiner系~(3，6，22)构造的图的一个自同构群，WITT[3]定义了一个Steiner系~(d，Rn，n)是由n个点组成的集合S及其子集的集合B(这里称为块)，使得每个块恰好包含m个点，每个d点集恰好包含在一个块中。Witt[4]证明了Steiner系统~(3，6，22)的存在，并且证明了它们在同构意义下是唯一的。An~(3，6，22)的自同构群Mz2包含作为指标2的子群的Mathieu群Mz2，是M22在M24中的正规化子。
The group G of the title is obtained as a primitive permutation group of degree 100 in which the stabilizer of a point has orbits of lengths 1, 22 and 77 and is isomorphic to the Mathieu group M22. Thus G has rank 3 in the sense of [1]. G is an automorphism group of a graph constructed from the Steiner system~(3, 6, 22).WITT [3] defined a Steiner system~(d, rn, n) to be a set S of n points together with a set B of subsets of S (referred to here as blocks) such that each block contains exactly m points and each set of d points is contained in exactly one block. WITT [4] showed that Steiner systems~(3, 6, 22) exist and that they are unique up to isomorphism. The automorphism group Mz2 of an~(3, 6, 22) contains the Mathieu group Mz2 as a subgroup of index 2 and is the normalizer of M22 in M24.