×

On growth of Grigorchuk groups. (English) Zbl 1024.20031

Summary: We present an analytic technique for estimating the growth for groups of intermediate growth. We apply our technique to Grigorchuk groups, which are the only known examples of such groups. Our estimates generalize and improve various bounds by Grigorchuk, Bartholdi and others.

MSC:

20F05 Generators, relations, and presentations of groups
20E08 Groups acting on trees
68R15 Combinatorics on words
Full Text: DOI

References:

[1] Adel’son-Velskii G. M., S.) 12 (6) pp 131– (1957)
[2] DOI: 10.1155/S1073792898000622 · Zbl 0942.20027 · doi:10.1155/S1073792898000622
[3] Grigorchuk R. I., Soviet Math. Dokl. 28 (1) pp 23– (1983)
[4] DOI: 10.1070/IM1985v025n02ABEH001281 · Zbl 0583.20023 · doi:10.1070/IM1985v025n02ABEH001281
[5] DOI: 10.1070/SM1986v054n01ABEH002967 · Zbl 0583.20024 · doi:10.1070/SM1986v054n01ABEH002967
[6] DOI: 10.1007/BF02471762 · Zbl 0949.20033 · doi:10.1007/BF02471762
[7] DOI: 10.1007/BF02698687 · Zbl 0474.20018 · doi:10.1007/BF02698687
[8] DOI: 10.1007/BF01158402 · Zbl 0595.20030 · doi:10.1007/BF01158402
[9] Ufnarovskij V. A., Berlin pp 1– (1995)
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.