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On the functional graph of the power map over finite groups

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Claudio Qureshi, Lucas Reis

Discrete Mathematics · Submitted 1 Jul 2021

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

The authors' main claim We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper.

how it is stated · asserted 1.00 read the record →

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arXiv ID2107.00584 (version 2)
Pith IDZUBQ2LAC, Pith's permanent record of this paper and its review
CitationClaudio Qureshi, Lucas Reis. "On the functional graph of the power map over finite groups." arXiv:2107.00584 (2021). https://pith.science/paper/ZUBQ2LAC
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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, 4,955 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.83 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper. Unlike the abelian case where all the trees associated with periodic points are isomorphic, in the case of flower groups we prove that several different classes of trees can occur. The class of central trees (i.e. associated with periodic points that are in the center of the group) are in general non-elementary and a recursive description is given in this work. Flower groups include many non abelian groups such as dihedral and generalized quaternion groups, and the projective general linear group of order two over a finite field. In particular, we provide improvements on past works regarding the description of the dynamics of the power map over these groups.

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 In this paper we study the description of the functional graphs associated with the power maps over finite groups. contribution 0.68 0.80 0.05 asserted 0.76
s1 We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper. contribution 0.57 0.95 0.52 asserted 1.00
s2 Unlike the abelian case where all the trees associated with periodic points are isomorphic, in the case of flower groups we prove that several different classes of trees can occur. result 0.99 0.91 0.22 asserted 1.00
s3 The class of central trees (i.e. associated with periodic points that are in the center of the group) are in general non-elementary and a recursive description is given in this work. result 0.79 0.93 0.12 asserted 0.99
s4 Flower groups include many non abelian groups such as dihedral and generalized quaternion groups, and the projective general linear group of order two over a finite field. contribution 0.41 0.38 0.06 asserted 0.99
s5 In particular, we provide improvements on past works regarding the description of the dynamics of the power map over these groups. contribution 0.87 0.87 0.10 asserted 0.99

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

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  • references and citing sentences
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  • P abstract
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  • 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

In this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper. Unlike the abelian case where all the trees associated with periodic points are isomorphic, in the case of flower groups we prove that several different classes of trees can occur. The class of central trees (i.e. associated with periodic points that are in the center of the group) are in general non-elementary and a recursive description is given in this work. Flower groups include many non abelian groups such as dihedral and generalized quaternion groups, and the projective general linear group of order two over a finite field. In particular, we provide improvements on past works regarding the description of the dynamics of the power map over these groups.

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