On the girth of finitely generated groups

✍ Scribed by Azer Akhmedov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 199 KB
• Volume: 268
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00375-2

✦ Synopsis

We study the notion of girth for finitely generated groups. It is proved that if the girth is 'small' then the group necessarily satisfies a law. A general construction is presented which provides examples of groups with infinite girth not containing nonabelian free group. We also prove that SL(n, Z) has infinite girth.