### On conjugacy classes in compact groups

Algebra Seminar

25th January 2023, 2:30 pm – 3:30 pm

Fry Building, G.13

It is a classical result of Landau that the number of conjugacy classes of a finite group G tends to infinity as |G| tends to infinity. For infinite groups we don't have any lower bound in general. However the situation is different for compact groups. In my talk I will present a proof that an infinite compact Hausdorff group has uncountably many conjugacy classes. The proof depends on a number of classical results on finite groups and their automorphisms. This is joint work with Andrei Jaikin-Zapirain.

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