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RESEARCH PRODUCT

Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39

Dieter HeldMario Osvin Pavčević

subject

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 groupMathematics

description

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.

yearjournalcountryeditionlanguage
1997-05-01European Journal of Combinatorics
https://doi.org/10.1006/eujc.1996.0103