Symbolic computation of Schur multipliers with an application to the groups of order dividing $p^6$

Abstract

We describe an algorithm to compute the Schur multipliers of all nilpotent Lie p-rings in the family defined by a symbolic nilpotent Lie p-ring. Symbolic nilpotent Lie p-rings can be used to describe the isomorphism types of p-groups of order p n for n ≤ 7 and all primes p ≥ n. We apply our algorithm to compute the Schur multipliers of all p-groups of order dividing p 6 .