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Examination shows Kazhdan's property (T) in automorphisms of free algebras, indicating connections to alternating groups.
We prove that, for the free algebra over a sufficiently rich operad O , a large subgroup of its group of tame automorphisms has Kazhdan’s property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.
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Bartholdi et al. (2025) studied this question.
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