On the prime graph question for integral group rings of Conway simple groups. (November 2019)

• Record Type: Journal Article
• Authors: Margolis, Leo
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 162
• Page End: 176
• Publication Date: 2019-11
• Subjects: primary 16U60 16S34 -- secondary 20C05 20C20 05E10; Unit group -- Group ring -- Prime graph question -- Sporadic simple groups; 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.2019.02.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The Prime Graph Question for integral group rings asks if it is true that if the normalized unit group of the integral group ring of a finite group G contains an element of order pq, for some primes p and q, also G contains an element of that order. We answer this question for the three Conway sporadic simple groups after reducing it to a combinatorial question about Young tableaux and Littlewood-Richardson coefficients. This finishes work of V. Bovdi, A. Konovalov and S. Linton.