Powerfully solvable and powerfully simple groups

Iker de las Heras; Gunnar Traustason

doi:10.1016/j.jpaa.2021.106714

Powerfully solvable and powerfully simple groups

Iker de las Heras, Gunnar Traustason

Department of Mathematical Sciences

University of the Basque Country

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

49 Downloads (Pure)

Abstract

We introduce the notion of a powerfully solvable group. These are powerful groups possessing an abelian series of a special kind. These groups include in particular the class of powerfully nilpotent groups. We will also see that for a certain rich class of powerful groups we can naturally introduce the term powerfully simple group and prove a Jordan-Hölder type theorem that justifies the term.

Original language	English
Article number	106714
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	8
Early online date	19 Feb 2021
DOIs	https://doi.org/10.1016/j.jpaa.2021.106714
Publication status	Published - 31 Aug 2021

Bibliographical note

Funding Information:
The first author is supported by the Spanish Government grant MTM2017-86802-P , partly with FEDER funds, and by the Basque Government grant IT974-16 . He is also supported by a predoctoral grant of the University of the Basque Country .

Publisher Copyright:
© 2021 Elsevier B.V.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Funding

The first author is supported by the Spanish Government grant MTM2017-86802-P , partly with FEDER funds, and by the Basque Government grant IT974-16 . He is also supported by a predoctoral grant of the University of the Basque Country .

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2021.106714

PSolvSimpleNEW.PDFAccepted author manuscript, 294 KBLicence: CC BY-NC-ND

Cite this

@article{b785824326274ad8b80a37666f1dc96a,

title = "Powerfully solvable and powerfully simple groups",

abstract = "We introduce the notion of a powerfully solvable group. These are powerful groups possessing an abelian series of a special kind. These groups include in particular the class of powerfully nilpotent groups. We will also see that for a certain rich class of powerful groups we can naturally introduce the term powerfully simple group and prove a Jordan-H{\"o}lder type theorem that justifies the term.",

author = "{de las Heras}, Iker and Gunnar Traustason",

note = "Funding Information: The first author is supported by the Spanish Government grant MTM2017-86802-P , partly with FEDER funds, and by the Basque Government grant IT974-16 . He is also supported by a predoctoral grant of the University of the Basque Country . Publisher Copyright: {\textcopyright} 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = aug,

day = "31",

doi = "10.1016/j.jpaa.2021.106714",

language = "English",

volume = "225",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier B.V.",

number = "8",

}

TY - JOUR

T1 - Powerfully solvable and powerfully simple groups

AU - de las Heras, Iker

AU - Traustason, Gunnar

N1 - Funding Information: The first author is supported by the Spanish Government grant MTM2017-86802-P , partly with FEDER funds, and by the Basque Government grant IT974-16 . He is also supported by a predoctoral grant of the University of the Basque Country . Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/8/31

Y1 - 2021/8/31

N2 - We introduce the notion of a powerfully solvable group. These are powerful groups possessing an abelian series of a special kind. These groups include in particular the class of powerfully nilpotent groups. We will also see that for a certain rich class of powerful groups we can naturally introduce the term powerfully simple group and prove a Jordan-Hölder type theorem that justifies the term.

AB - We introduce the notion of a powerfully solvable group. These are powerful groups possessing an abelian series of a special kind. These groups include in particular the class of powerfully nilpotent groups. We will also see that for a certain rich class of powerful groups we can naturally introduce the term powerfully simple group and prove a Jordan-Hölder type theorem that justifies the term.

UR - http://www.scopus.com/inward/record.url?scp=85101422523&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2021.106714

DO - 10.1016/j.jpaa.2021.106714

M3 - Article

AN - SCOPUS:85101422523

SN - 0022-4049

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 8

M1 - 106714

ER -

Powerfully solvable and powerfully simple groups

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this