Abstract: Given a Polish group G and a class C of subgroups of G, define a subgroup L in C to be a "universal C subgroup of G" if every subgroup H in C is a pre-image of L, via a continuous endomorphism of G. I will give context for this definition and, in particular, justify the use of the word "universal". After summarizing my results on universal subgroups, I will prove that the countable power of any Polish group contain universal analytic and co-analytic subgroups.

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