6533b7cffe1ef96bd125993d
RESEARCH PRODUCT
Multiplicative loops of 2-dimensional topological quasifields
Giovanni FalconeÁGota FigulaKarl Strambachsubject
CollineationAlgebraic structureDimension (graph theory)Topology01 natural sciencesSection (fiber bundle)TermészettudományokFOS: MathematicsCollineation groupLocally compact space0101 mathematicsMatematika- és számítástudományokMathematicsAlgebra and Number TheoryGroup (mathematics)010102 general mathematicsMultiplicative function20N05 22A30 12K99 51A40 57M60Lie groupMathematics - Rings and AlgebrasSections in Lie group010101 applied mathematicsTranslation planes and speadsMultiplicative loops of locally compact quasifieldRings and Algebras (math.RA)Settore MAT/03 - Geometriadescription
We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a $1$-dimensional compact subgroup. In the last section we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension $4$ admitting an at least $7$-dimensional Lie group as collineation group.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-07-04 |