Groups whose orders factorise into at most four primes. (January 2022)

• Record Type: Journal Article
• Authors: Dietrich, Heiko; Eick, Bettina; Pan, Xueyu
• Is Part Of: Journal of symbolic computation. Volume 108(2022)
• Page Start: 23
• Page End: 40
• Publication Date: 2022-01
• Subjects: Group determination -- Group enumeration -- SmallGroup database; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.04.005
• Languages: English
• ISSNs: 0747-7171

Abstract

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.