Abstract
Let G = 〈G1 ·〉 be a group definable in an o-minimal structure M.. A subset // of G is G-definable if H is definable in the structure 〈G1 ·〉 (while definable means definable in the structure M). Assume G has no G-definable proper subgroup of finite index. In this paper We prove that if G has no nontrivial abelian normal subgroup, then G is the direct product of G-definable subgroups H1,... ,Hk such that each Hi is definably isomorphic to a semialgebraic linear group over a definable real closed field. As a corollary we obtain an o-minimal analogue of Cherlin's conjecture.
Original language | English |
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Pages (from-to) | 4397-4419 |
Number of pages | 23 |
Journal | Transactions of the American Mathematical Society |
Volume | 352 |
Issue number | 10 |
DOIs | |
State | Published - 2000 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics