Corrigendum to “On the dimension growth of groups”. (English) Zbl 1279.20053
From the text: It turned out that there are gaps in the proofs of several results from the paper mentioned in the title [ibid. 347, No. 1, 23-39 (2011; Zbl 1277.20051)]. We can prove these results only under some additional assumptions. Namely, we can prove the statements that the Thompson group \(F\) and some solvable groups of class 3 have exponential dimension growth assuming exponential control (i.e. exponential bounds on the sizes of \(\lambda\)-clusters). The result that every solvable finitely generated subgroup of \(F\) has polynomial dimension growth is true, though the argument presented in the paper had to be modified. Detailed proofs can be found in a revised version of the paper in the arXiv [see arXiv:1008.3868v4].
In this erratum, we give the main definitions and formulations from the revised version. We also list wrong and unproved statements from the original paper.
In this erratum, we give the main definitions and formulations from the revised version. We also list wrong and unproved statements from the original paper.
MSC:
| 20F69 | Asymptotic properties of groups |
| 20F65 | Geometric group theory |
| 54F45 | Dimension theory in general topology |
| 57M07 | Topological methods in group theory |
| 20F05 | Generators, relations, and presentations of groups |
| 05C63 | Infinite graphs |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
Keywords:
dimension growth; groups with infinite asymptotic dimension; Thompson group \(F\); Ehrhart polynomials; quasi-isometry invariants; finitely presented groups; amenable groupsCitations:
Zbl 1277.20051References:
| [1] | Dranishnikov, Alexander; Sapir, Mark, On the dimension growth of groups, J. Algebra, 347, 1, 23-39 (2011) · Zbl 1277.20051 |
| [2] | Dranishnikov, Alexander; Sapir, Mark, On the dimension growth of groups · Zbl 1277.20051 |
| [3] | Gromov, Mikhail, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS), 1, 2, 109-197 (1999) · Zbl 0998.14001 |
| [4] | Parry, Walter, Growth series of some wreath products, Trans. Amer. Math. Soc., 331, 2, 751-759 (1992) · Zbl 0793.20034 |
| [5] | Ozawa, Narutaka, Metric spaces with subexponential asymptotic dimension growth, Int. J. Algebra Comput., 22, 2 (2012), Article ID 1250011 · Zbl 1238.54015 |
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