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A Nunke type classification in the locally compact setting

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Samuel M. Corson, Olga Varghese

Group Theory · Submitted 26 Dec 2019

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

The authors' main claim In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -- if and only if G is torsion-free and does not include Q or the p-adic integers Zp for any prime p.

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arXiv ID1912.11867 (version 1)
Pith IDZS64R3TZ, Pith's permanent record of this paper and its review
CitationOlga Varghese, Samuel M. Corson. "A Nunke type classification in the locally compact setting." arXiv:1912.11867 (2019). https://pith.science/paper/ZS64R3TZ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,341 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.91 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -- if and only if G is torsion-free and does not include Q or the p-adic integers Zp for any prime p. This mirrors a classical characterization given by Nunke for slender abelian groups.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -- if and only if G is torsion-free and does not include Q or the p-adic integers Zp for any prime p. result 0.95 0.93 0.96 asserted 1.00
s1 This mirrors a classical characterization given by Nunke for slender abelian groups. background 0.61 0.08 0.03 asserted 1.00

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

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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

In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -- if and only if G is torsion-free and does not include Q or the p-adic integers Zp for any prime p. This mirrors a classical characterization given by Nunke for slender abelian groups.

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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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