Demir, S2024-07-182024-07-1820040046-5755https://doi.org/10.1023/B:GEOM.0000024722.31926.97https://hdl.handle.net/11411/8907Let G denote the isometry group of a regular tree of degree greater than or equal to3. The notion of congruence subgroup is introduced and finite generation of the congruence Hecke algebras is proven. Let U be congruence subgroup and M(G; U) be the category of smooth representations of G generated by their U-fixed vectors. We also show that this subcategory is closed under taking subquotients. All these results are analogues of well-known results in the case of p-adic groups. It is also shown that the category of admissible representation of G is Noetherian in the sense that every subrepresentation of a finitely generated admissible representation is again finitely generated. Since we want to emphesize the similarities between these groups and p-adic groups, we give the same proofs which also work in the p-adic case whenever possible.eninfo:eu-repo/semantics/closedAccessCategory Of Smooth Representationsİsometry Groups Of Regular TreesNoetherian CategoriesUniform AdmissibilityArticle2-s2.0-384311456310.1023/B:GEOM.0000024722.31926.972071Q2189105Q2WOS:000220927900012