A Kazhdan group with an infinite outer automorphism group

Abstract

D. Kazhdan has introduced in 1967 the Property (T) for local compact groups (see [D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1967)]). In this article we prove that for n ≥ 3 and m ∈ ℕ the group SLn (K)⋉ℳn,m(K) is a Kazhdan group having the outer automorphism group infinite.

Keywords

• Representations of topological groups
• Kazhdan Property (T)
• Mautner's lemma