Special Moufang sets, their root groups and their μ-maps

Tom De Medts; Yoav Segev; Katrin Tent

doi:10.1112/plms/pdm059

Special Moufang sets, their root groups and their μ-maps

Tom De Medts, Yoav Segev, Katrin Tent

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We prove Timmesfeld's conjecture that special abstract rank one groups are quasisimple. We give two characterizations of the root groups in special Moufang sets: a normal subgroup of the point stabilizer is a root group if it is either regular, or nilpotent and transitive. We prove that if a root group of a special Moufang set contains an involution, then it is of exponent 2. We also show that the root groups are abelian if and only if the so-called μ-maps are involutions.

Original language	English
Pages (from-to)	767-791
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	96
Issue number	3
DOIs	https://doi.org/10.1112/plms/pdm059
State	Published - 1 Jan 2008

ASJC Scopus subject areas

General Mathematics

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abstract = "We prove Timmesfeld's conjecture that special abstract rank one groups are quasisimple. We give two characterizations of the root groups in special Moufang sets: a normal subgroup of the point stabilizer is a root group if it is either regular, or nilpotent and transitive. We prove that if a root group of a special Moufang set contains an involution, then it is of exponent 2. We also show that the root groups are abelian if and only if the so-called μ-maps are involutions.",

author = "{De Medts}, Tom and Yoav Segev and Katrin Tent",

note = "Funding Information: The first author is a Postdoctoral Fellow of the Research Foundation – Flanders (Belgium) (FWO – Vlaanderen). The second author is partially supported by BSF grant no. 2004-083. The third author is partially supported by DFG under SFB 701. Part of this work was done while the first two authors were guests of the University of Bielefeld and were also partially supported by the DFG under SFB 701.",

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N2 - We prove Timmesfeld's conjecture that special abstract rank one groups are quasisimple. We give two characterizations of the root groups in special Moufang sets: a normal subgroup of the point stabilizer is a root group if it is either regular, or nilpotent and transitive. We prove that if a root group of a special Moufang set contains an involution, then it is of exponent 2. We also show that the root groups are abelian if and only if the so-called μ-maps are involutions.

AB - We prove Timmesfeld's conjecture that special abstract rank one groups are quasisimple. We give two characterizations of the root groups in special Moufang sets: a normal subgroup of the point stabilizer is a root group if it is either regular, or nilpotent and transitive. We prove that if a root group of a special Moufang set contains an involution, then it is of exponent 2. We also show that the root groups are abelian if and only if the so-called μ-maps are involutions.

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Special Moufang sets, their root groups and their μ-maps

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