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Computing the Schur multipliers of the Lie p-rings in the family defined by a symbolic Lie p-ring presentation
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 pn 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 pn for all primes p and n7. 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 p6 for all primes p5. Via the Lazard correspondence this yields the Schur multipliers of all groups of order dividing p6 for all primes p5.



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pñ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pñ对于所有素数pñ7。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p6 对于所有素数 p5。通过Lazard对应关系,可以得出所有阶数除法组的Schur乘法器p6 对于所有素数 p5

更新日期:2021-01-08
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