Multiplicative Loops of 2-Dimensional Topological Quasifields. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Falcone, Giovanni; Figula, Ágota; Strambach, Karl
• Is Part Of: Communications in algebra. Volume 44:Issue 6(2016)
• Page Start: 2592
• Page End: 2620
• Publication Date: 2016-06-02
• Subjects: Collineation groups -- Multiplicative loops of locally compact quasifields -- Sections in Lie groups -- Translation planes and speads; 20N05 -- 22A30 -- 12K99 -- 51A40 -- 57M60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1053905
• Languages: English
• ISSNs: 0092-7872

Abstract

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.