Journal of Symbolic Computation ( IF 0.7 ) Pub Date : 2021-01-05 , DOI: 10.1016/j.jsc.2020.12.003 Bettina Eick , Taleea Jalaeeyan Ghorbanzadeh
A symbolic Lie p-ring presentation defines a family of nilpotent Lie rings with 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 for all primes p and . 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 for all primes . Via the Lazard correspondence this yields the Schur multipliers of all groups of order dividing for all primes .
中文翻译:
计算谎言的舒尔乘数p型圈通过一个象征性的谎言所定义的家庭p型圈呈现
具有代表性的Lie p环表示定义了一个幂等Lie环族,其中无限多个素数p和固定正整数n的元素。符号Lie p环表示用于阶幂幂Lie环的同构类型分类对于所有素数p和。我们描述了一种算法,该算法可计算符号Lie p环表示所定义的族中所有幂零Lie环的Schur乘数。我们将其应用于确定所有阶除的零幂李环的Schur乘子 对于所有素数 。通过Lazard对应关系,可以得出所有阶数除法组的Schur乘法器 对于所有素数 。