Finite core-pp-groups

✍ Scribed by G. Cutolo; E.I. Khukhro; J.C. Lennox; J. Wiegold; S. Rinauro; H. Smith

• Book ID: 102572246
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 210 KB
• Volume: 188
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.6811

✦ Synopsis

For n a positive integer, a group G is called core-n if HrH has order at most n G Ž for every subgroup H of G where H is the normal core of H, the largest normal G . subgroup of G contained in H . It is proved that a finite core-p p-group G has a normal abelian subgroup whose index in G is at most p 2 if p / 2, which is the best possible bound, and at most 2 6 if p s 2.