## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

Bohr sets and multiplicative Diophantine approximationVolume 167, Number 9 (2018)
Affine Hecke algebras and raising operators for Macdonald polynomialsVolume 93, Number 1 (1998)
A tameness criterion for Galois representations associated to modular forms $(\mod p)$Volume 61, Number 2 (1990)
The central limit theorem for dependent random variablesVolume 15, Number 3 (1948)
Universal dynamics for the defocusing logarithmic Schrödinger equationVolume 167, Number 9 (2018)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935--
• Access: By subscription only
• Euclid URL: https://projecteuclid.org/dmj

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MR Citation Database MCQ (2016): 2.29
JCR (2016) Impact Factor: 2.171
JCR (2016) Five-year Impact Factor: 2.417
JCR (2016) Ranking: 10/310 (Mathematics)
Article Influence (2016): 3.852
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2016): 4.467

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### Featured article

#### On finiteness properties of the Johnson filtrations

Volume 167, Number 9 (2018)
##### Abstract

Let $\Gamma$ be either the automorphism group of the free group of rank $n\geq4$ or the mapping class group of an orientable surface of genus $n\geq12$ with at most $1$ boundary component, and let $G$ be either the subgroup of $\mathrm{IA}$-automorphisms or the Torelli subgroup of $\Gamma$. For $N\in\mathbb{N}$ denote by $\gamma_{N}G$ the $N$th term of the lower central series of $G$. We prove that

(i) any subgroup of $G$ containing $\gamma_{2}G=[G,G]$ (in particular, the Johnson kernel in the mapping class group case) is finitely generated;

(ii) if $N=2$ or $n\geq8N-4$ and $K$ is any subgroup of $G$ containing $\gamma_{N}G$ (for instance, $K$ can be the $N$th term of the Johnson filtration of $G$), then $G/[K,K]$ is nilpotent and hence the Abelianization of $K$ is finitely generated;

(iii) if $H$ is any finite-index subgroup of $\Gamma$ containing $\gamma_{N}G$, with $N$ as in (ii), then $H$ has finite Abelianization.