Finitely generated groups with polynomial index growth

✍ Scribed by Pyber, László; Segal, Dan

• Book ID: 118740421
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2007
• Tongue: English
• Weight: 318 KB
• Volume: 2007
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2007.087

✦ Synopsis

We prove that a finitely generated soluble residually finite group has polynomial index growth if and only if it is a minimax group. We also show that if a finitely generated group with PIG is residually finite-soluble then it is a linear group. These results apply in particular to boundedly generated groups; they imply that every infinite BG residually finite group has an infinite linear quotient.