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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: [email protected]
RICHARD M. WEISS
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A. e-mail: [email protected]
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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

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