Search results for "Orbit structure"

showing 4 items of 4 documents

Some Hadamard designs with parameters (71,35,17)

2002

Up to isomorphisms there are precisely eight symmetric designs with parameters (71, 35, 17) admitting a faithful action of a Frobenius group of order 21 in such a way that an element of order 3 fixes precisely 11 points. Five of these designs have 84 and three have 420 as the order of the full automorphism group G. If |G| = 420, then the structure of G is unique and we have G = (Frob21 × Z5):Z4. In this case Z(G) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z7. If |G| = 84, then Z(G) is of order 2, and in precisely one case a Sylow 2-subgroup is elementary abelian. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 144–149, 2002; DOI 10.1002/jcd.996

Combinatoricssymmetric design; Hadamard design; orbit structure; automorphism groupInner automorphismSylow theoremsStructure (category theory)Discrete Mathematics and CombinatoricsOuter automorphism groupOrder (group theory)Abelian groupElement (category theory)Frobenius groupMathematicsJournal of Combinatorial Designs
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Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39

1997

AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.

Discrete mathematicsKlein four-groupG-moduleQuaternion groupAlternating groupOuter automorphism groupGroup representationsymmetric design; Frobenius group; orbit structureTheoretical Computer ScienceCombinatoricsComputational Theory and MathematicsSymmetric groupDiscrete Mathematics and CombinatoricsGeometry and TopologyFrobenius groupMathematicsEuropean Journal of Combinatorics
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Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19

2001

Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.

Group (mathematics)Existential quantificationOrbit structureAutomorphismAction (physics)Automorphism groupOrbit structureTheoretical Computer ScienceCombinatoricsHadamard transformHadamard design; Automorphism group; Tactical decomposition; Orbit structureHadamard designDiscrete Mathematics and CombinatoricsOrder (group theory)Tactical decompositionHadamard matrixMathematicsDiscrete Mathematics
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A Series of Hadamard Designs with Large Automorphism Groups

2000

Abstract Whilst studying a certain symmetric (99, 49, 24)-design acted upon by a Frobenius group of order 21, it became clear that the design would be a member of an infinite series of symmetric (2q2 + 1, q2, (q2 − 1)/2)-designs for odd prime powers q. In this note, we present the definition of the series and give some information about the automorphism groups of its members.

incidence matrixAlgebra and Number TheoryOuter automorphism groupAlternating groupAutomorphismCombinatoricsInner automorphismSymmetric groupOrder (group theory)symmetric design; Hadamard matrix; incidence matrix; orbit structureHadamard matrixFrobenius grouporbit structuresymmetric designHadamard matrixMathematicsJournal of Algebra
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