A characterization of the Higman-Sims simple group
نویسندگان
چکیده
منابع مشابه
Torsion Units in Integral Group Ring of Higman-sims Simple Group
Let V (ZG) be the normalized unit group of the integral group ring ZG of a finite group G. One of most interesting conjectures in the theory of integral group ring is the conjecture (ZC) of H. Zassenhaus [25], saying that every torsion unit u ∈ V (ZG) is conjugate to an element in G within the rational group algebra QG. For finite simple groups, the main tool of the investigation of the Zassenh...
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We introduce some well known results about permutation groups, strongly regular graphs, design theory and finite geometry. Our goal is the construction of the Higman-Sims group as an index 2 subgroup of the automorphism group of a (100, 22, 0, 6)-srg. To achieve this we introduce some tools from design theory. Some of the arguments here are slightly more general than those given in lectures. Al...
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The Higman-Sims design is an incidence structure of 176 points and 176 blocks of cardinality 50 with every two blocks meeting in 14 points. The automorphism group of this design is the Higman-Sims simple group. We demonstrate that the point set and the block set of the Higman-Sims design can be partitioned into subsets X1, X2, . . . , X11 and B1, B2, . . . , B11, respectively, so that the subst...
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Recently there has been substantial progress towards computing the mod 2 cohomology of low rank sporadic simple groups. In fact the mod 2 cohomology of every sporadic simple group not containing (Z/2) has been computed, with the notable exceptions of HS (the Higman–Sims group) and Co3 (one of the Conway groups). The reason for these exceptions is that these two groups have large and complicated...
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We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z4 × Z5 × Z5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson’s pentagonpentagram definition of the Hoffman-Singleton graph and is obtained by studying maximum cocliques of the Hoffman-Singleton graph in Robertson’s parametrisation. Th...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1969
ISSN: 0021-8693
DOI: 10.1016/0021-8693(69)90114-8