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We determine the algebraic structure of the multiplicative loops for locallycompact $2$-dimensional topological connected quasifields. In particular, ourattention turns to multiplicative loops which have either a normal subloop ofpositive dimension or which contain a $1$-dimensional compact subgroup. In thelast section we determine explicitly the quasifields which coordinatize locallycompact translation planes of dimension $4$ admitting an at least$7$-dimensional Lie group as collineation group.

Multiplicative loops of $2$-dimensional topological quasifields