The Characterization of Ree Groups 2F4(q) by Their Element Orders

✍ Scribed by Huiwen Deng; Wujie Shi

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 77 KB
• Volume: 217
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7808

✦ Synopsis

All Ree groups F q are characterized by their element orders. ᮊ 1999 Aca- 4 demic Press Ž . For any group G, denote by G the set of all element orders of G. e Ž . Clearly, G is a partially ordered set under the divisibility relation. e Ž . Ž Ž . . Given a finite resp., infinite group G, let h G be the number of e Ž . isomorphism classes of finite resp., infinite groups with the same set Ž . Ž Ž .. G of element orders. It is clear that h G G 1 for any group G. e e In terms of function h, groups G are classified as follows: Ž Ž .. DEFINITION 1. A group G is called irrecognizable if h G s ϱ e Ž . infinity ; otherwise G is called recognizable. In addition, a recognizable Ž Ž .. group G is called a k-recognizable group if h G s k. Usually, a e 1-recognizable group is called a characterizable group.