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

Gourion Catherine | Zendy

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

Author(s) -

Gourion Catherine

Publication year - 1999

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610798006905

Subject(s) - mathematics , transitive relation , automorphism , countable set , combinatorics , isomorphism (crystallography) , regular polygon , chain (unit) , group (periodic table) , pure mathematics , outer automorphism group , prime (order theory) , automorphism group , crystallography , chemistry , physics , geometry , organic chemistry , astronomy , crystal structure

We characterise all maximal convex l ‐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 l ‐group A (Ω). Finally, assuming the Continuum Hypothesis, we show that there exists an unbounded chain of proper prime subgroups of A (Ω).

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