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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In group theory, the growth rate of a group with respect to a symmetric generating set describes the size of balls in the group. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of length n.As an immediate corollary of this inequality we get that the growth rate does not depend on the choice of generating set.