Almost All Generalized Extraspecial p-Groups Are Resistant

✍ Scribed by Radu Stancu

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 90 KB
• Volume: 249
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9069

✦ Synopsis

A p-group P is called resistant if, for any finite group G having P as a Sylow p-subgroup, the normalizer N G P controls p-fusion in G. The aim of this paper is to prove that any generalized extraspecial p-group P is resistant, excepting the case when P = E × A, where A is elementary abelian and E is dihedral of order 8 (when p = 2) or extraspecial of order p 3 and exponent p (when p is odd). This generalizes a result of Green and Minh.