A generalization of the Higman-Sims technique
نویسندگان
چکیده
منابع مشابه
Tight Subdesigns of the Higman-sims Design
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...
متن کاملOn the Graphs of Hoffman-Singleton and Higman-Sims
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...
متن کاملa generalization of strong causality
در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...
On the Codes Related to the Higman-Sims Graph
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...
متن کاملStrongly regular graphs and the Higman-Sims group
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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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1978
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(78)80034-1