Abstract
B. H. Neumann (5) has shown, by using free products with an amalgamated subgroup, that every group can be embedded in a divisible group. This theorem can also be proved, in an entirely different way, by making use of the wreath product (Baumslag(1)). In view of this connexion between roots in groups and the wreath product, a study is made here of the conditions which ensure that the wreath product (and also the unrestricted wreath product) shares certain properties regarding the existence and uniqueness of roots with the groups from which it is composed.
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