Computing the Schur multipliers of the Lie p-rings in the family defined by a symbolic Lie p-ring presentation. (September 2021)

• Record Type: Journal Article
• Authors: Eick, Bettina; Ghorbanzadeh, Taleea Jalaeeyan
• Is Part Of: Journal of symbolic computation. Volume 106(2021)
• Page Start: 68
• Page End: 77
• Publication Date: 2021-09
• Subjects: Schur multiplier -- Lie ring -- p-group; 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.2020.12.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A symbolic Lie p -ring presentation defines a family of nilpotent Lie rings with p n elements for infinitely many primes p and a fixed positive integer n . Symbolic Lie p -ring presentations are used in the classification of isomorphism types of nilpotent Lie rings of order p n for all primes p and n ≤ 7 . We describe an algorithm to compute the Schur multipliers of all nilpotent Lie rings in the family defined by a symbolic Lie p -ring presentation. We apply this to determine the Schur multipliers of all nilpotent Lie rings of order dividing p 6 for all primes p ≥ 5 . Via the Lazard correspondence this yields the Schur multipliers of all groups of order dividing p 6 for all primes p ≥ 5 .