Another Existence and Uniqueness Proof for the Higman-Sims Simple Group

• 来源期刊: 代数集刊(英文版)
• 关键词: sporadic simple groups computational methods representations
• 年，卷（期）: 2005,（3）
• 页码范围: 369-398
• 页数: 30页
• 语种: 英文

摘要

In this article, we give a short proof for the existence and uniqueness of the Higman-Sims sporadic simple group HS by means of the first author's algorithm [17] and uniqueness criterion [18], respectively. We realize HS as a subgroup of GL22(11), and determine its automorphism group Aut(HS). We also give a presentation for Aut(HS) in terms of generators and relations. Furthermore, the character table of HS is determined and representatives of its conjugacy classes are given as short words in its generating matrices inside GL22(11).