In 1997, Grigorchuk and de la Harpe suggested computing the growth series for the Baumslag-Solitar group BS(2,3). After 25 years, this is still an open problem. In fact, the growth of only the solvable groups BS(1,n) and automatic groups BS(n,n) are known. In this talk I will review what has since been discovered about these remarkable groups and conclude with new unpublished results concerning the exponents of growth for the subfamily BS(2,2n).
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