Special rank one groups with abelian unipotent subgroups are perfect

2011/08/31 by Steinbach, Anja
#20E42 (51E42) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1108.6189

Abstract

T. De Medts, Y. Segev and K. Tent [Special Moufang sets, their root groups and their μ-maps, Proc. Lond. Math. Soc. (3) 96 (2008), 767-791] proved that the little projective group of a special Moufang set M(U,τ) is perfect provided that U has size at least 4. We give a short, elementary and self-contained argument when U is abelian, working with Timmesfeld's concept of special (abstract) rank one groups with abelian unipotent subgroups [Abstract root subgroups and simple groups of Lie type, Monographs in Mathematics, 95. Birkhäuser, 2001]. This simplifies Timmesfeld's (quasi) simplicity criterion for groups generated by abstract root subgroups [loc. cit., II (2.14)].

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