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We show that the automorphism group of Philip Hall's universal locally finitegroup has ample generics,that is, it admits comeager diagonal conjugacy classesin all dimensions.Consequently, it has the small index property, is not theunion of a countable chain of non-open subgroups, and has the automaticcontinuity property. Also, we discuss some algebraic and topological propertiesof the automorphism group of Hall universal group. For example, we show thatevery generic automorphism of Hall universal group is conjugate to all of itspowers, and hence has roots of all orders.

Hall universal group has ample generic automorphisms