Characterization of Alternating Groups by Orders of Normalizers of Sylow Subgroups

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: alternating group Sylow subgroup normalizer
• 年，卷（期）: 2001,（3）
• 页码范围: 249-256
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

In this paper, we prove that a finite group G is isomorphic to the alternating group An if and only if the normalizers of their p-Sylow subgroups have the same order for every prime p. Moreover, if n ≥ 4 with n ≠ 8,10 and r is the greatest prime not exceeding n, then a finite group G is isomorphic to An if and only if |G| = |An| and the normalizers of their r-Sylow subgroups have the same order.