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Journal of the London Mathematical Society 1999 59(2):407-421; doi:10.1112/S0024610798006905
© 1999 by London Mathematical Society
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© The London Mathematical Society

Maximal Convex Subgroups of the Automorphism Group of a Doubly Transitive Chain

Catherine Gourion

Equipe de Logique Mathématique Tour 45–55, 5ème Étage, Case 7012, Université Paris VII 2 place Jussieu, 75251 Paris Cedex 05, France gourion{at}logique.jussieu.fr

Received 12 August 1996. Revision received 29 January 1997.

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


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