Abstract

The replacement property (or Steinitz Exchange Lemma) for vector spaces has a natural analog for finite groups and their generating sets. For the special case of the groups $\text{PSL}(2,p),$ where p is a prime larger than 5, first partial results concerning the replacement property were published by Benjamin Nachman (2014 Nachman, B. (2014). Generating sequences of $\text{PSL}(2,p).$ J. Group Theory 17(6):925–945.[Crossref], [Web of Science ®] , [Google Scholar]). Second partial results were published by Hy P.G. Lam (2017 Lam, H. P. G. The replacement property of PSL$(2,p)$ and PSL$(2,p^2).$ arXiv e-Prints. page arXiv:1709.08745, September 2017. [Google Scholar]). The main goal of this paper is to provide a complete answer for $\text{PSL}(2,p).$

摘要

向量空间的替换性质（或 Steinitz 交换引理）与有限群及其生成集有一个自然的类比。对于组的特殊情况$\text{PSL}(2,磷),$其中 p 是一个大于 5 的质数，关于替换性质的第一部分结果由 Benjamin Nachman ( 2014)发表 Nachman, B.（2014 年）。生成序列 $\text{PSL}(2,磷).$ J. 群论17(6): 925 – 945。[Crossref]、[Web of Science®]、[  Google Scholar]）。Hy PG Lam (2017)发表了第二部分结果 Lam, HPG PSL 的置换特性$(2,磷)$ 和PSL$(2,{磷}^2).$ arXiv 电子打印。第 arXiv 页：1709.08745，2017 年 9 月。 [谷歌学术]）。本文的主要目的是提供一个完整的答案$\text{PSL}(2,磷).$