On the Higman-Sims simple group of order 44, 352, 000
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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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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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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All linear codes of length 100 over a field F which admit the Higman-Sims simple group HS in its rank 3 representation are determined. By group representation theory it is proved that they can all be understood as submodules of the permutation module FΩ where Ω denotes the vertex set of the Higman-Sims graph. This module is semisimple if charF 6= 2, 5 and absolutely indecomposable otherwise. Al...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90262-4