Harada Group Uniquely Determined by Centralizer of a 2-Central Involution

• 来源期刊: 代数集刊（英文版）
• 关键词: strong uniqueness Harada group concrete character table
• 年，卷（期）: 2003,（3）
• 页码范围: 303-372
• 页数: 70页
• 语种: 英文

摘要

In this article we show that the sporadic simple Harada group G is uniquely determined up to isomorphism by the centralizer CG(z) of a 2-central involution z of G. This strengthens Y. Segev's uniqueness theorem [24] which required the known structure of the centralizers of two non-conjugate involutions.Using the second author's algorithm [19], we also provide a self-contained existence proof for the Harada group G by giving matrix generators inside GL133(19).Furthermore, the character table of G is determined and representatives for the conjugacy classes of the group are given as short words in the generating matrices.