Talambutsa, A. L. Attainability of the exponent of exponential growth in free products of cyclic groups. (English. Russian original) Zbl 1108.20032 Math. Notes 78, No. 4, 569-572 (2005); translation from Mat. Zametki 78, No. 4, 614-618 (2005). Summary: The set of exponents of exponential growth (growth exponents) for a finitely generated group with respect to all possible generators of this group is studied. It is proved that the greatest lower bound of this set is attained for the free products of a cyclic group of prime order and a free group of finite rank. Cited in 2 Documents MSC: 20F05 Generators, relations, and presentations of groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations Keywords:generators of groups; finitely generated groups; exponential growth; growth exponents; reduced words; free products of cyclic groups; Nielsen transformations; free groups PDFBibTeX XMLCite \textit{A. L. Talambutsa}, Math. Notes 78, No. 4, 569--572 (2005; Zbl 1108.20032); translation from Mat. Zametki 78, No. 4, 614--618 (2005) Full Text: DOI References: [1] P. de la Harpe, Topics in Geometric Group Theory, Univ. of Chicago Press, Chicago, 2000. · Zbl 0965.20025 [2] A. Sambusetti, ”Minimal growth of non-Hopfian free products,” C. R. Acad. Sci. Paris Ser. I, 329 (1999), 943–946. · Zbl 0998.20030 [3] G. Arzhantseva and I. Lysionok, ”Growth tightness for word hyperbolic groups,” Math. Z., 241 (2002), 597–611. · Zbl 1045.20035 [4] J. S. Wilson, ”On exponential and uniformly exponential growth for groups,” Invent. Math., 155 (2004), no. 2, 287–303. · Zbl 1065.20054 [5] R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. · Zbl 0368.20023 [6] W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory. Presentations of Groups in Terms of Generators and Relations, Dover Publications, Inc., New York, 1976. · Zbl 0362.20023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.