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Finitely presented subgroups of automatic groups and their isoperimetric functions

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Gilbert Baumslag, Martin Bridson, Charles Miller, Hamish Short

Group Theory · Submitted 6 May 1996

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

The authors' main claim This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic.

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arXiv IDmath/9605201 (version 1)
Pith IDOZPNJGZF, Pith's permanent record of this paper and its review
CitationCharles Miller, Gilbert Baumslag, Hamish Short, Martin Bridson. "Finitely presented subgroups of automatic groups and their isoperimetric functions." arXiv:math/9605201 (1996). https://pith.science/paper/OZPNJGZF
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,861 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.81 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.

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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 describe a general technique for embedding certain amalgamated products into direct products. method 0.58 0.91 0.12 asserted 1.00
s1 This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. result 0.64 0.92 0.58 asserted 0.94
s2 We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality. result 0.91 0.89 0.21 asserted 0.62

What kind of paper the classifier reports this is: method or tool 0.86 · 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

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.

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