Growth Rate (group Theory)

DEFINITION Suppose ''G'' is a finitely generated group; and ''T'' is a finite ''symmetric'' set of Generator s (symmetric means that if $x \in T$ then $x^{-1} \in T$ ). Any element $x \in G$ can be expressed as a Word in the ''T''-alphabet : $x = a_1 \cdot a_2 \cdot \ldots \cdot a_k \mbox{ where } a_i\in T$ Let us consider the subset of all elements of ''G'' which can be presented by such a word of length ≤''n''
	:<math>B N(G,T)	\{x\in G d(x, e)\le n\}</math>
	:<math>\#(n)	B_n(G,T), </math>

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