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- Title
Residual dimension of nilpotent groups.
- Authors
Pengitore, Mark
- Abstract
The function FG(n) gives the maximum order of a finite group needed to distinguish a nontrivial element of G from the identity with a surjective group morphism as one varies over nontrivial elements of word length at most n. In previous work [M. Pengitore, Effective separability of finitely generated nilpotent groups, New York J. Math. 24 2018, 83–145], the author claimed a characterization for FN(n) when N is a finitely generated nilpotent group. However, a counterexample to the above claim was communicated to the author, and consequently, the statement of the asymptotic characterization of FN(n) is incorrect. In this article, we introduce new tools to provide lower asymptotic bounds for FN(n) when N is a finitely generated nilpotent group. Moreover, we introduce a class of finitely generated nilpotent groups for which the upper bound of the above article can be improved. Finally, we construct a class of finitely generated nilpotent groups N for which the asymptotic behavior of FN(n) can be fully characterized.
- Subjects
FINITE groups; NILPOTENT groups; MORPHISMS (Mathematics); GROUP identity
- Publication
Journal of Group Theory, 2020, Vol 23, Issue 5, p801
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2019-0117