Premium
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).