Small cancellation and outer automorphisms of Kazhdan groups acting on hyperbolic spaces

2023/04/15 by Chifan, I., Ioana, A., Osin, D. +1 · 3 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2304.07455

Abstract

We show that every finite group realizes as the outer automorphism group of an ICC hyperbolic group with Kazhdan property (T). This result complements the well-known theorem of Paulin stating that the outer automorphism group of every hyperbolic group with property (T) is finite. We also show that, for every countable group Q, there exists an acylindrically hyperbolic group G with property (T) such that Out(G)≅ Q. The proofs employ strengthened versions of some previously known results in small cancellation theory.

Cited by

• Boundary actions of outer automorphism groups of Thompson-like groups
• Stability, approximable quotients, and higher property (T)
• On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups

Related

• Small cancellation in acylindrically hyperbolic groups
• A Kazhdan group with an infinite outer automorphism group
• Rips construction and Kazhdan property (T)
• Kazhdan groups with infinite outer automorphism group
• A note on quotients of word hyperbolic groups with Property (T)