Abstract. It is shown that every profirdte torsion group has a finite series of closed characteristic subgroups in which each factor either is a pro-p-group for some prime p or is isomorphic to a Cartesian product of isomorphic finite simple groups.
w 1. IntroductionIt has been known for some time that all compact Hausdorff torsion groups are profinite. A proof of this result may be found in [3], p. 69. Examples of infinite profinite torsion groups are provided by, for instance, Cartesian products of finite groups of bounded exponent, with the product topology. In [2], HERFORT has shown that if G is a profinite torsion group then the set ~ (G) ofprimesp for which G has non-trivial Sylow p-subgroups is finite. Here we use this result, the results of HALL and HIGMAN [1] and the classification of the finite simple groups to establish a stronger statement: Theorem 1. Let G be a compact Hausdorff torsion group. Then G has a finite series