Homeomorphism groups of degree-one compact ordinals are uniformly perfect and strongly distorted with classified normal generators, while higher-degree cases split as semidirect products with computed abelianizations.
Bertram, On a theorem of Schreier and Ulam for countable permutations, J
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Algebraic and geometric properties of homeomorphism groups of ordinals
Homeomorphism groups of degree-one compact ordinals are uniformly perfect and strongly distorted with classified normal generators, while higher-degree cases split as semidirect products with computed abelianizations.