Profinite and Finite Groups Associated with Loop and Diffeomorphism Groups of Non-Archimedean Manifolds

$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed compact groups is studied. Representations of such profinite groups are discused.