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arXiv · 1507.01137

Multiplicative loops of $2$-dimensional topological quasifields

Giovanni Falcone·Ágota Figula·Karl Strambach
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Abstract

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.

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Giovanni Falcone, Ágota Figula, Karl Strambach. 2015-07-04. Multiplicative loops of $2$-dimensional topological quasifields. https://arxiv.org/abs/1507.01137

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