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On the action of the Hua subgroups in special Moufang sets

Published online by Cambridge University Press:  01 January 2008

YOAV SEGEV  and
RICHARD M. WEISS
YOAV SEGEV
Affiliation:
Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel. e-mail: yoavs@math.bgu.ac.il
RICHARD M. WEISS
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A. e-mail: rweiss@tufts.edu
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Abstract

We show that in a special Moufang set, either the root groups are elementary abelian 2-groups, or the Hua subgroup H (= the Cartan subgroup) acts “irreducibly” on U, i.e. the only non-trivial H-invariant subgroup of a root group normalized by H is the whole root group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 77 - 84
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[DS]Medts, T. De and Segev, Y.. Identities in Moufang sets, submitted.CrossRefGoogle Scholar
[DW]Medts, T. De and Weiss, R. M.. Moufang sets and Jordan division algebras. To appear in Math. Ann.Google Scholar
[FT]Feit, W. and Thompson, J. G.. Solvability of groups of odd order. Pacific J. Mat 13 (1963), 775–1029.CrossRefGoogle Scholar
[Su]Suzuki, M.. Finite groups of even order in which Sylow 2-groups are independent. Ann. of Math. (2) 80 (1964), 58–77.CrossRefGoogle Scholar
[Ti]Timmesfeld, F.. Abstract root subgroups and simple groups of Lie type. 2001 Monogr. Math 95 (Birkhäuser-Verlag, 2001).Google Scholar
[TW]Tits, J. and Weiss, R. M.. Moufang polygons. Monogr. Math. (Springer-Verlag, 2002).CrossRefGoogle Scholar