Open subgroups of $p$-adic algebraic groups
Group Theory
2023-05-01 v1 Logic
Abstract
In \cite{Pillay} and more formally in \cite{Onshuus-Pillay} it was asked whether open subgroups of -adic algebraic groups are (-adic) semialgebraic, equivalently, definable in the structure . We give a positive answer in the commutative case. Together with results of \cite{Prasad} this leads to a positive answer for reductive algebraic groups.
Cite
@article{arxiv.2304.14798,
title = {Open subgroups of $p$-adic algebraic groups},
author = {Anand Pillay and Ningyuan Yao},
journal= {arXiv preprint arXiv:2304.14798},
year = {2023}
}