On the condensation property of the Lamplighter groups and groups of intermediate growth

• Date: 2018
• Main Authors: Benli, Mustafa Gökhan, Grigorchuk, Rostislav
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Lamplighter groups; groups of intermediate growth; space of marked groups; condensation groups; 20F65; 20E08; 20F69; 20F05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1032
• Journal Title: Algebra and Discrete Mathematics

The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group \(L=\mathbb{Z}_2 \wr  \mathbb{Z}\)  is a condensation group and has a minimal presentation by generators and relators. The condensat...