Zariski Dense Subgroups of Semisimple Algebraic Groups with Isomorphic p-adic Closures | Synapse
March 29, 2026Open Access
Zariski Dense Subgroups of Semisimple Algebraic Groups with Isomorphic p-adic Closures
Key Points
The primary aim is to establish conditions for the finiteness of isomorphism classes of Zariski dense subgroups in semisimple algebraic groups with isomorphic p-adic closures.
Demonstrated theoretical proofs under natural conditions.
Analyzed structural properties of semisimple algebraic groups.
Explored relationships between group structures and p-adic closures.
Found that under specified conditions, only a finite number of isomorphism classes exist.
Established connections efficiently between Zariski dense subgroups and p-adic properties.
Abstract
We prove under certain natural conditions the finiteness of the number of isomorphism classes of Zariski dense subgroups in semisimple groups with isomorphic p -adic closures.