Counting p-groups and Lie algebras using PORC formulae

JOURNAL OF ALGEBRA

卷:545

Article

关键词: p-groups;    Lie algebras;    Counting problems;    PORC;   

DOI  :  10.1016/j.jalgebra.2019.02.034

来源: Elsevier

【 摘 要 】

Counting problems whose solution is PORC were introduced in a famous paper by Higman (1960). We consider two specific counting problems with PORC solutions: the number of isomorphism types of d-generator class-2 Lie algebras over F-q (as a function in q) and the number of isomorphism types of d-generator p-class 2 p-groups (as a function in p). We prove lower bounds for the degrees of their PORC formulae for all d is an element of N and we determine explicit PORC formulae for d <= 7. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free