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A normal form for a free product of groups is a representation or choice of a reduced sequence for each element in the free product . Normal Form Theorem for Free Product of Groups. Consider the free product of two groups and . Then the following two equivalent statements hold. (1) If , where is a reduced sequence, then in.
Free product. In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “ universal ” group having these properties, in the sense that any two ...
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