Computing the Schur multipliers of the Lie p-rings in the family defined by a symbolic Lie p-ring presentation. (September 2021) - Eick, Bettina; Ghorbanzadeh, Taleea Jalaeeyan
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 .