Conjugacy classes and growth conditions

✍ Scribed by Roberto Incitti

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 98 KB
• Volume: 265
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00029-2

✦ Synopsis

In this paper we show using a purely combinatorial argument that a finitely generated infinite group such that f E (n) an s , where a is a constant, admits for every a sequence {g i, } of non-unit elements whose centralizer contains more than i 1/2-elements of length less than i. Of course, the interest of this result is in the fact that it excludes the possibility that the group is a pure torsion group, since otherwise the existence of the sequence {g i, } is obvious. As an application of this result, we show that, in the case where r < 3/2, there exists an element whose centralizer has finite index in G.