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Complete growth series and products of groups. (English) Zbl 1223.20032
Summary: The property of having a rational complete growth series is shown to be preserved by direct and graph products, as well as certain free products with amalgamation. These results extend earlier work of Alonso, Chiswell and Lewin.
MSC:
20F65 Geometric group theory
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups
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