Permutation groups | Infinite group theory

Hall's universal group

In algebra, Hall's universal group isa countable locally finite group, say U, which is uniquely characterized by the following properties. * Every finite group G admits a monomorphism to U. * All such monomorphisms are conjugate by inner automorphisms of U. It was defined by Philip Hall in 1959, and has the universal property that all countable locally finite groups embed into it. (Wikipedia).

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Related pages

Monomorphism | Permutation | Symmetric group | Locally finite group | Cayley's theorem | Algebra | Direct limit | Inner automorphism