Impact Factor: 0.5

Veröffentlicht seit 1. Januar 1998

Journal of Group Theory

ISSN: 1435-4446

Editors-in-Chief: Timothy C. Burness, Christopher W. Parker

Managing Editors: John S. Wilson, Evgeny I. Khukhro

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.

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Group Theory
Representation Theory of Groups
Computational Aspects of Group Theory
Combinatorics and Graph Theory
Algebra and Number Theory

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Band 26 Heft 6

November 2023

Öffentlich zugänglich 1. November 2023

Frontmatter

Seiten: i-iv

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Öffentlich zugänglich 13. Juni 2023

The Higman operations and embeddings of recursive groups

Vahagn H. Mikaelian

Seiten: 1067-1093

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Abstract

In the context of Higman embeddings of recursive groups into finitely presented groups, we suggest an approach, termed the 𝐻-machine, which for certain wide classes of groups allows constructive Higman embeddings of recursive groups into finitely presented groups. The approach is based on Higman operations, and it explicitly constructs some specific recursively enumerable sets of integer sequences arising during the embeddings. Specific auxiliary operations are introduced to make the work with Higman operations a simpler and more intuitive procedure. Also, an automated mechanism of constructive embeddings of countable groups into 2-generator groups preserving certain “patterns” is mentioned.

Open Access 22. Juni 2023

Redundant relators in cyclic presentations of groups

Ihechukwu Chinyere, Gerald Williams

Seiten: 1095-1126

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Abstract

A cyclic presentation of a group is a presentation with an equal number of generators and relators that admits a particular cyclic symmetry. We characterise the orientable, non-orientable, and redundant cyclic presentations and obtain concise refinements of these presentations. We show that the Tits alternative holds for the class of groups defined by redundant cyclic presentations and show that if the number of generators of the cyclic presentation is greater than two, then the corresponding group is large. Generalising and extending earlier results of the authors, we describe the star graphs of orientable and non-orientable cyclic presentations and classify the cyclic presentations whose star graph components are pairwise isomorphic incidence graphs of generalised polygons, thus classifying the so-called ( m , k , ν ) (m,k,\nu) -special cyclic presentations.

23. Juni 2023

Commutator endomorphisms of totally projective abelian 𝑝-groups

Patrick Keef

Seiten: 1127-1141

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Abstract

For a primary abelian group 𝐺, Chekhlov and Danchev (2015) defined three variations of Kaplansky’s notion of full transitivity by restricting one’s attention to the sub group , the sub ring and the unitary subring of the endomorphism ring of 𝐺 generated by the collection of all commutator endomorphisms. They posed the problem of describing exactly which totally projective groups exhibit these forms of full transitivity. This problem, and some closely related questions, are completely answered using the Ulm function of 𝐺.

Open Access 25. März 2023

Algebraic groups over finite fields: Connections between subgroups and isogenies

Davide Sclosa

Seiten: 1143-1155

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Abstract

Let 𝐺 be a linear algebraic group defined over a finite field F q \mathbb{F}_{q} . We present several connections between the isogenies of 𝐺 and the finite groups of rational points ( G ⁢ ( F q n ) ) n ≥ 1 (G(\mathbb{F}_{\smash{q^{n}}}))_{n\geq 1} . We show that an isogeny ϕ : G ′ → G \phi\colon G^{\prime}\to G over F q \mathbb{F}_{q} gives rise to a subgroup of fixed index in G ⁢ ( F q n ) G(\mathbb{F}_{\smash{q^{n}}}) for infinitely many 𝑛. Conversely, we show that if 𝐺 is reductive, the existence of a subgroup H n H_{n} of fixed index 𝑘 for infinitely many 𝑛 implies the existence of an isogeny of order 𝑘. In particular, we show that the infinite sequence H n H_{n} is covered by a finite number of isogenies. This result applies to classical groups GL m \mathrm{GL}_{m} , SL m \mathrm{SL}_{m} , SO m \mathrm{SO}_{m} , SU m \mathrm{SU}_{m} , Sp 2 ⁢ m \mathrm{Sp}_{2m} and can be extended to non-reductive groups if 𝑘 is prime to the characteristic. As a special case, we see that if 𝐺 is simply connected, the minimal indices of proper subgroups of G ⁢ ( F q n ) G(\mathbb{F}_{\smash{q^{n}}}) diverge to infinity. Similar results are investigated regarding the sequence ( G ⁢ ( F p ) ) p (G(\mathbb{F}_{p}))_{p} by varying the characteristic 𝑝.

19. September 2023

Relative stable equivalences of Morita type for the principal blocks of finite groups and relative Brauer indecomposability

Naoko Kunugi, Kyoichi Suzuki

Seiten: 1157-1184

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Abstract

We discuss representations of finite groups having a common central 𝑝-subgroup 𝑍, where 𝑝 is a prime number. For the principal 𝑝-blocks, we give a method of constructing a relative 𝑍-stable equivalence of Morita type, which is a generalization of stable equivalence of Morita type and was introduced by Wang and Zhang in a more general setting. Then we generalize Linckelmann’s results on stable equivalences of Morita type to relative 𝑍-stable equivalences of Morita type. We also introduce the notion of relative Brauer indecomposability, which is a generalization of the notion of Brauer indecomposability. We give an equivalent condition for Scott modules to be relatively Brauer indecomposable, which is an analog of that given by Ishioka and the first author.

8. Juni 2023

5-Regular prime graphs of finite nonsolvable groups

Qinghong Guo, Weijun Liu, Lu Lu

Seiten: 1185-1214

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Abstract

The prime graph Δ ⁢ ( G ) \Delta(G) of a finite group 𝐺 is a graph whose vertex set is the set of prime factors of the degrees of all irreducible complex characters of 𝐺, and two distinct primes 𝑝 and 𝑞 are joined by an edge if the product p ⁢ q pq divides some character degree of 𝐺. In 2014, Tong-Viet [H. P. Tong-Viet, Finite groups whose prime graphs are regular, J. Algebra 397 (2014), 18–31] proposed the following conjecture. Let 𝐺 be a group and let k ≥ 5 k\geq 5 be odd. If the prime graph Δ ⁢ ( G ) \Delta(G) is 𝑘-regular, then Δ ⁢ ( G ) \Delta(G) is a complete graph of order k + 1 k+1 . In this paper, we show that if the prime graph Δ ⁢ ( G ) \Delta(G) of a finite nonsolvable group 𝐺 is 5-regular, then Δ ⁢ ( G ) \Delta(G) is isomorphic to the complete graph K 6 K_{6} or possibly the graph depicted in the first figure below. Moreover, if 𝐺 is an almost simple group, then Δ ⁢ ( G ) \Delta(G) is isomorphic to the complete graph K 6 K_{6} .

15. Juni 2023

On weak commutativity in 𝑝-groups

Raimundo Bastos, Emerson de Melo, Ricardo de Oliveira, Carmine Monetta

Seiten: 1215-1229

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Abstract

The weak commutativity group χ ⁢ ( G ) \chi(G) is generated by two isomorphic groups 𝐺 and G φ G^{\varphi} subject to the relations [ g , g φ ] = 1 [g,g^{\varphi}]=1 for all g ∈ G g\in G . We present new bounds for the exponent of χ ⁢ ( G ) \chi(G) and its sections, when 𝐺 is a finite 𝑝-group.

Öffentlich zugänglich 27. Juni 2023

More on chiral polytopes of type \{4, 4, …, 4\} with~solvable automorphism groups

Wei-Juan Zhang

Seiten: 1231-1265

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Abstract

In a 2021 paper, Conder et al. constructed two infinite families of chiral 4-polytopes of type { 4 , 4 , 4 } \{4,4,4\} with solvable automorphism groups. Here we present a general construction for chiral polytopes of type { 4 , 4 , … , 4 } \{4,4,\dots,4\} with rank 4, 5 and 6, which are obtained as Boolean covers of the unique tight regular polytope of the same type.

Ahead-of-Print / Just-Accepted

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Band 1 (1998)

Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
5-year Journal Impact Factor	0.6	2022, Journal Citation Reports (Clarivate, 2023)
Journal Citation Indicator	0.49	2022, Journal Citation Reports (Clarivate, 2023)
CiteScore	1.1	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.633	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	1.202	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.54

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Submission

Manuscripts should be submitted online using the Journal of Group Theory submission site at https://mc.manuscriptcentral.com/jgroupt.

Submission process

For the initial submission, authors are asked to upload a PDF file via the submission link above. Please do not submit source files for manuscripts until requested to do so. However, when papers are accepted, source files will be needed. These will need to be compressed or "zipped" to be uploaded to the system. Please keep formatting macros to a minimum, to make conversion of files more accurate. Do not worry about chapter headings, running titles, bad page breaks, etc. and avoid adding extra space and using glue to improve the appearance of the manuscript. Please ensure that the material has been carefully proof-read and that all input and style files used are made available to the publishers.

Figures or Graphics. Figures created via a graphics package should be saved in encapsulated PostScript (EPS) format. A separate file for each graphic should be submitted. In a TEX document, EPS files may be incorporated into the TEX file by using one of the standard macro packages.

Footnotes. Footnotes should be kept to a minimum and be as brief as possible. They should be numbered consecutively and placed at the foot of the page to which they refer.

References. References should be collected at the end of the paper and numbered in alphabetical order of the authors’ names. Titles of journals should be abbreviated as in Mathematical Reviews. The following examples show the preferred style for references to a book, a preprint that has appeared on arXiv, a paper in a journal, a paper
in a proceedings volume, and an unpublished dissertation.

[1] J. L. Alperin. Local representation theory (Cambridge University Press, 1986).
[2] C. Bonnafe´ and M. J. Dyer. Semidirect product decomposition of Coxeter groups. Preprint (2008). http://arxiv.org/abs/0805.4100.
[3] W. Feit and J. G. Thompson. Solvability of groups of odd order. Pacific J. Math. 13 (1963), 774–1029.
[4] G. Higman. Some non-simplicity criteria for finite groups. In Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Math. 372 (Springer-Verlag, 1974), pp. 367–376.
[5] J. D. King. Finite presentability of Lie algebras and pro-p groups. Ph.D. thesis. University of Cambridge (1995).

Authors will receive a PDF file of the page proofs for correction. Only typographical errors should be corrected in the proofs. If excessive alterations to the original manuscript are requested after the paper has been typeset, the authors will be charged for the cost of resetting.

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In this journal, authors have the option to publish their article under an open access license. Open Access allows you as an author to retain copyright and share your findings with colleagues and interested parties worldwide without any restraints.
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Editorial

Editors-in-Chief

Timothy C. Burness, University of Bristol (UK)
Christopher Parker, University of Birmingham (UK)

Managing Editors

Evgeny Khukhro, University of Lincoln (UK) and Sobolev Institute of Mathematics (Russia)
John S. Wilson, University of Oxford (UK)

Editorial Board

Olivier Dudas, Institut de Mathématiques de Marseille (France)
Bettina Eick, TU Braunschweig (Germany)
Michael Giudici, The University of Western Australia (Australia)
Robert Guralnick, University of Southern California (USA)
Adrian Ioana, University of California, San Diego (USA)
Benjamin Klopsch, Heinrich-Heine-Universität (Germany)
Anton Klyachko, Moscow State University (Russia)
Dessislava H. Kochloukova, Cidade Universitária "Zeferino Vaz" (Brazil)
Andrea Lucchini, Università di Padova (Italy)
Frank Lübeck, RWTH Aachen (Germany)
Cheryl Praeger, The University of Western Australia (Australia)
Rachel Skipper, ENS Paris (France)
Britta Späth, Bergische Universität Wuppertal (Germany)
Hung Tong-Viet, Binghamton University (USA)
George Willis, University of Newcastle (Australia)

(English)

Online ISSN: 1435-4446
Print ISSN: 1433-5883
Typ: Zeitschrift
Sprache: Englisch
Verlag: De Gruyter
Erstveröffentlichung: 1. Januar 1998
Erscheinungsweise: 6 Hefte pro Jahr
Zielgruppe: Researchers interested in Group Theory