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On the replacement property for PSL(2,p)
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-06-12 , DOI: 10.1080/00927872.2021.1933999
David Cueto Noval 1, 2 , Aidan A. Lorenz 2, 3 , Baran Zadeoğlu 2, 4
Affiliation  

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 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 PSL(2,p). J. Group Theory 17(6):925945.[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,p2). arXiv e-Prints. page arXiv:1709.08745, September 2017. [Google Scholar]). The main goal of this paper is to provide a complete answer for PSL(2,p).



中文翻译:

关于 PSL(2,p) 的替换性质

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PSL(2,),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 PSL(2,). J. 群论17(6): 925945[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,) 和PSL(2,2). 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PSL(2,).

更新日期:2021-06-12
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