Groups whose orders factorise into at most four primes

Heiko Dietrich; Bettina Eick; Xueyu Pan

doi:10.1016/j.jsc.2021.04.005

Groups whose orders factorise into at most four primes

Heiko Dietrich, Bettina Eick, Xueyu Pan

School of Mathematics

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

1 Citation (Scopus)

Abstract

The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.

Original language	English
Pages (from-to)	23-40
Number of pages	18
Journal	Journal of Symbolic Computation
Volume	108
DOIs	https://doi.org/10.1016/j.jsc.2021.04.005
Publication status	Published - Jan 2022

Keywords

Group determination
Group enumeration
SmallGroup database

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10.1016/j.jsc.2021.04.005

Cite this

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title = "Groups whose orders factorise into at most four primes",

abstract = "The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.",

keywords = "Group determination, Group enumeration, SmallGroup database",

author = "Heiko Dietrich and Bettina Eick and Xueyu Pan",

note = "Funding Information: The first author was supported by an Australian Research Council grant DP190100317 . The third author was supported by an Australian RTP scholarship; part of this work is based on the MPhil thesis of the third author, see Pan (2021) . The authors thank Mike Newman for various helpful discussions. Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2022",

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doi = "10.1016/j.jsc.2021.04.005",

language = "English",

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AU - Eick, Bettina

AU - Pan, Xueyu

N1 - Funding Information: The first author was supported by an Australian Research Council grant DP190100317 . The third author was supported by an Australian RTP scholarship; part of this work is based on the MPhil thesis of the third author, see Pan (2021) . The authors thank Mike Newman for various helpful discussions. Publisher Copyright: © 2021 Elsevier Ltd Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2022/1

Y1 - 2022/1

N2 - The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.

AB - The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.

KW - Group determination

KW - Group enumeration

KW - SmallGroup database

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JO - Journal of Symbolic Computation

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SN - 0747-7171

ER -

Groups whose orders factorise into at most four primes

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Keywords

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Computing with Lie groups and algebras: nilpotent orbits and applications

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Groups whose orders factorise into at most four primes

Abstract

Keywords

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Computing with Lie groups and algebras: nilpotent orbits and applications

Cite this