The primitive distance-transitive representations of the Fischer groups.
Linton, Stephen A., Lux, Klaus, Soicher, Leonard H. (1995)
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Linton, Stephen A., Lux, Klaus, Soicher, Leonard H. (1995)
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Norman Purzitsky (1972)
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Peter J. Cameron (1972)
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We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite...
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