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Special Moufang sets, their root groups and their μ‐maps
Author(s) -
De Medts Tom,
Segev Yoav,
Tent Katrin
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm059
Subject(s) - mathematics , abelian group , nilpotent , conjecture , transitive relation , root (linguistics) , pure mathematics , rank (graph theory) , involution (esoterism) , combinatorics , philosophy , linguistics , politics , political science , law
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.