Residual Dimension of Finitely Generated Nilpotent Groups
Abstract
In previous work, the author claimed an effective characterization for residual finiteness and lower asymptotic bounds for conjugacy separability of all finitely generated nilpotent groups. However, a counterexample to the characterization of residual finiteness for finitely generated nilpotent groups was communicated to the author which also had consequences to the lower asymptotic bound provided for conjugacy separability for the class of finitely generated nilpotent groups. Subsequently, the statements of the asymptotic characterization of residual finiteness and the asymptotic lower bound for conjugacy separability for the same class of groups along with their proofs are incorrect. In this article, we provide correct asymptotic bounds for residual finiteness and asymptotic lower bounds for conjugacy separability for the class of finitely generated nilpotent groups. We additional provide upper asymptotic bounds for conjugacy separability for the class of finitely generated nilpotent groups.
Degree
Ph.D.
Advisors
McReynolds, Purdue University.
Subject Area
Mathematics
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