Growth of groups

Growth functions of groups have been studied intensively in geometric group theory.  Regarded up to affine rescaling, they give a group invariant called the growth rate, and there are long-standing questions about possible growth rates for finitely generated groups.  Another stream of questions asks whether the growth values satisfy a recursion, a property which is called rational growth and depends on the choice of generators.  I will survey the area and discuss the classic proofs that hyperbolic groups and virtually abelian groups have rational growth in any generators

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