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MAXIMAL CONVEX SUBGROUPS OF THE AUTOMORPHISM GROUP OF A DOUBLY TRANSITIVE CHAIN

Published online by Cambridge University Press:  01 April 1999

CATHERINE GOURION
CATHERINE GOURION
Affiliation:
Equipe de Logique Mathématique, Tour 45–55, 5ème Étage, Case 7012, Université Paris VII, 2 place Jussieu, 75251 Paris Cedex 05, France; gourion@logique.jussieu.fr
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Abstract

We characterise all maximal convex [lscr ]-subgroups of A(Ω), the automorphism group of a doubly transitive chain Ω of countable coterminality. We then determine, up to isomorphism, all doubly transitive actions of the [lscr ]-group A(Ω). Finally, assuming the Continuum Hypothesis, we show that there exists an unbounded chain of proper prime subgroups of A(Ω).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 407 - 421
Copyright
The London Mathematical Society 1999

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