Compact torsion groups and finite exponent

On the structure of compact torsion groups

“…Thus, for example, since the class of locally finite groups and the class of groups of finite exponent are both closed with respect to extensions, Theorem 1 implies the Corollary. ( The assertion (ii) also follows from the theorem of HSaVORT [2] mentioned above. We do not care to comment on the hypotheses in (i) and (ii), except to remark that all compact Hausdorff torsion groups of finite exponent are locally finite if and only if the restricted Burnside problem has a positive solution.…”

“…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.…”

Strong completeness in profinite groups

“…is a p-element and x is a p-element if and only if x = x {1>0) (see [4]). A net of elements {x a } of a profinite group G converges to an element x if for all open normal subgroups V of G, x a V -xV for almost all a.…”

On Pro-p Groups Admitting a Fixed-Point-Free Automorphism

“…A long-standing problem is whether any compact torsion group has a finite exponent. In [4] W. Herfort reduced this problem to the question of whether any torsion pro-p group has a finite exponent (see also [16]). In this context we shall prove the following theorem.…”