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W. Herfort:
"Compact Torsion Groups";
Talk: Universita Milano, Bicocca, Milano (invited); 2011-02-16.

A compact group in which every element has finite order is a "compact torsion group". It turns quickly out that such a group is profinite, i.e., the projective limit of finite groups. It is an open problem whether such a group has a finite exponent. For abelian G a proof is easy and so it is for solvable groups. A "reduction theorem" has been found in 1979 by the speaker which says that G has finite exponent if and only if its Sylows have finite exponent. I intend to give that short proof. It is a deep result of E.Zelmanov that every torsion pro-p group is locally finite, i.e., that every topologically finitely generated torsion pro-p group is actually finite. J.Wilson has used Zelmanov's and the speakers result to prove that every compact torsion

Kompakte Torsionsgruppen haben nur endlich viele "Primteiler"

Torsion groups, profinite groups

http://home.matapp.unimib.it/node/3112