Search results for "Semifield"

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Divisible designs from semifield planes

2002

AbstractWe give a general method to construct divisible designs from semifield planes and we use this technique to construct some divisible designs. In particular, we give the case of twisted field plane as an example.

Discrete mathematicsAutomorphism groupGeneral methodDivisible designsField (mathematics)Division (mathematics)Permutation groupTranslation (geometry)Plane (Unicode)Theoretical Computer ScienceR-permutation groupsCombinatoricsDiscrete Mathematics and CombinatoricsAutomorphism groupsTranslation planesDivision algebrasSemifieldMathematicsDiscrete Mathematics
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Multiplicative Loops of Quasifields Having Complex Numbers as Kernel

2017

We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to $$Spin_3({\mathbb {R}})$$ . Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.

Multiplicative loops of locally compact quasifields semifields sections in Lie groups translation planes automorphism groups.Applied Mathematics010102 general mathematicsMultiplicative functionDimension (graph theory)Lie groupField (mathematics)Translation (geometry)01 natural sciences010101 applied mathematicsCombinatoricsKernel (algebra)Mathematics (miscellaneous)Locally compact spaceSettore MAT/03 - Geometria0101 mathematicsComplex numberMathematics
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