Abstract. Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a group in a very obvious way. This new group is called the external direct product of the groups Gi from the collection Γ. On the other hand we have the internal direct product of subgroups of a group. For a finite collection the internal direct product of subgroups is isomorphic with the external direct product. It is no longer true when the collection is infinite, even countable. For an infinite collection of groups the direct product must be defined in the other way. The main purpose of this paper is to give a general concept of the direct product of an arbitrary collection of groups, which is called THE COMPLETE DIRECT PRODUCT OF GROUPS.
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