A Relation in Free Products
A comparative study which contrasts the theory of free groups with the theory of free products has some general interest. One area where comparison can sometimes be made in an elementary way concerns relations, and their consequences: for example, the consequences of the relation XY = YX . It has been known for some years that, in a free group, this relation is a consequence of the relation of X 2 Y 2 Z 2 = 1 . We now consider the analogous situation for free products.
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