Construction of the Rudvalis group of order 145,926,144,000

Conway, James; Wales, David B.

doi:10.1016/0021-8693(73)90063-x

Cited by 29 publications

(16 citation statements)

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“…Since we have 3 = 84, 4 = 24, 5 = 6 and 6 = 24/19 by Proposition 2.4, we see that the maximum coclique designs of are 2, 3, 4 or 5-designs. By computation with MAGMA, we verified that the maximum coclique designs of are 5-(24, 9,6) designs.…”

Section: The 2 11 : M 24 -Graph Codes and Hadamard Matricesmentioning

confidence: 80%

On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

Horiguchi

Kitazume

Nakasora

2009

J of Combinatorial Designs

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In this article, we consider the maximum cocliques of the 2 11 :M 24 -graph K. We show that the maximum cocliques of size 24 of K can be obtained from two Hadamard matrices of size 24, and that there are exactly two maximum cocliques up to equivalence. We verify that the two nonisomorphic designs with parameters 5-(24,9,6) can be constructed from the maximum cocliques of K, and that these designs are isomorphic to the support designs of minimum weights of the ternary extended quadratic residue and Pless symmetry [24,12,9] codes. Further, we give a new construction of K from these 5-(24,9,6) designs. q

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Section: The 2 11 : M 24 -Graph Codes and Hadamard Matricesmentioning

confidence: 80%

On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

Horiguchi

Kitazume

Nakasora

2009

J of Combinatorial Designs

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“…It was originally constructed by J. H. Conway and D. B. Wales in its 28-dimensional projective representation by extending a representation of a maximal subgroup L 2 25 Á 2 2 (cf. [4,7]). A di¨erent construction of the same representation uses another maximal subgroup 2 6 Á G 2 2 (cf.…”

Section: Introductionmentioning

confidence: 96%

A construction of the simple group of Rudvalis from the group U₃(5):2

Coolsaet¹

1998

JGTH

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“…The case A » Ru. Let Ru be the simple group of order 214 • 33 • 53 • 7 • 13-29 whose existence was first proposed by Rudvalis and later confirmed by Conway and Wales [7]. The multiplier of Ru is known to have order 2 and the outer automorphism group is trivial (see [11]).…”

Section: Assuming That Tf Normalizes Tx and Again Invoking Our Hypothmentioning

confidence: 99%

Finite groups with a standard component whose centralizer has cyclic Sylow 2-subgroups

Finkelstein¹

1977

Proc. Amer. Math. Soc.

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Abstract. Let G be a finite group with 0(G) = \,A a standard component of G and X the normal closure of A in G. Furthermore, assume that C(A) has cyclic Sylow 2-subgroups. Then conditions are given on A which imply that either X = A or C(A) has Sylow 2-subgroups of order 2. These results are then applied to the cases where A is isomorphic to • 0 or Ru, the proper 2-fold covering of the Rudvalis group.

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Construction of the Rudvalis group of order 145,926,144,000

Cited by 29 publications

References 1 publication

On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

A construction of the simple group of Rudvalis from the group U₃(5):2

Finite groups with a standard component whose centralizer has cyclic Sylow 2-subgroups

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Construction of the Rudvalis group of order 145,926,144,000

Cited by 29 publications

References 1 publication

On the maximum cocliques of the rank 3 graph of 211 : M24

On the maximum cocliques of the rank 3 graph of 211 : M24

A construction of the simple group of Rudvalis from the group U3(5):2

Finite groups with a standard component whose centralizer has cyclic Sylow 2-subgroups

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On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

On the maximum cocliques of the rank 3 graph of 2¹¹ : M₂₄

A construction of the simple group of Rudvalis from the group U₃(5):2