Search results for "Klein four-group"

showing 2 items of 2 documents

A presentation and a representation of the Held group

1996

In this note we give a brief description of a new presentation of the Held group, which is deduced only from the original work of D. Held in 1969, who shows that a finite simple group, having the same centralizer of a 2-central involution as in the Mathieu group M24, is M24, L5(2) or a group of order 4.030.387.200. The first complete uniqueness proof for the latter case was given by L. Soicher in 1991. The generators and relations occurring here are easy to verify by a simple Todd–Coxeter algorithm. It is an easy task to get a new uniqueness and existence proof of the Held group from this result. Also basic facts like the Schur Multiplier or the automorphism group of the Held group follow f…

AlgebraPure mathematicsPresentation of a groupHeld groupG-moduleKlein four-groupSymmetric groupGeneral MathematicsQuaternion groupSchur multiplierMathematicsMathieu group M24Archiv der Mathematik
researchProduct

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
researchProduct