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An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product satisfies Kazhdan’s property (T) and when it satisfies some vastness properties including SQ-universality.

CONJUGATING AUTOMORPHISMS OF GRAPH PRODUCTS: KAZHDAN’S PROPERTY (T) AND SQ-UNIVERSALITY