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On subgroup separability of free-by-cyclic and deficiency 1 groups

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Monika Kudlinska

Group Theory · Submitted 10 Nov 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2211.05752 (version 2)
Pith ID2UNPSXGD, Pith's permanent record of this paper and its review
CitationMonika Kudlinska. "On subgroup separability of free-by-cyclic and deficiency 1 groups." arXiv:2211.05752 (2022). https://pith.science/paper/2UNPSXGD
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,282 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.11 · states quantitative result 0.31 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$. We also prove that random deficiency 1 groups are not subgroup separable with positive asymptotic probability.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$. result 0.99 0.95 0.58 asserted 1.00
s1 We also prove that random deficiency 1 groups are not subgroup separable with positive asymptotic probability. result 0.99 0.94 0.23 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$. We also prove that random deficiency 1 groups are not subgroup separable with positive asymptotic probability.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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