Journal of Algebra 523 (2019) 365–367
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Journal of Algebra
www.elsevier.com/locate/jalgebra
Corrigendum
Corrigendum to “Effective subgroup separability of
finitely generated nilpotent groups”
[J. Algebra 506 (2018) 489–508]
Jonas Deré
*
, Mark Pengitore
a r t i c l e i n f o a b s t r a c t
Article history:
Received 27 November 2018
Available online 21 January 2019
Communicated by Dan Segal
The purpose of this short note is to provide a correction to
the second statement of [1, Theorem 1.1].
© 2019 Elsevier Inc. All rights reserved.
All notation and terminology will be taken from [1]. We recall the second statement
of [1, Theorem 1.1] below.
Theorem 1. Let N be a torsion-free, finitely generated nilpotent group with a finite gen-
erating subset S. If H N is a normal subgroup of infinite index, there exists a constant
ψ(N, H) ∈ N such that
F
N,H,S
(n) ≈ (log(n))
ψ(N,H)
.
The proof of this theorem was in two steps. We first proved [1, Proposition 4.1] which
implies that F
N,H,S
(n) ≈ F
N
H
,{1},
¯
S
(n). We then appealed to a characterization of
F
N,{1},S
(n) for infinite, finitely generated nilpotent groups as given in [4, Theorem 1.1].
However, a counterexample to the latter result was communicated to the second author
DOI of original article: https://doi.org/10.1016/j.jalgebra.2018.03.035.
* Corresponding author.
E-mail address: jonas.dere@kuleuven.be (J. Deré).
https://doi.org/10.1016/j.jalgebra.2018.12.025
0021-8693/© 2019 Elsevier Inc. All rights reserved.