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

Date

2014-06-01

Author

Benli, Mustafa Gökhan

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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 = Z2 ≀ Z is a condensation group and has a minimal presentation by generators and relators. The condensation property is achieved by showing that L belongs to a Cantor subset of the space M2 of marked 2-generated groups consisting mostly of groups of intermediate growth.

Subject Keywords

Condensation groups, Groups of intermediate growth, Lamplighter groups, Space of marked groups

URI

http://adm.luguniv.edu.ua/
https://hdl.handle.net/11511/83755

Journal

ALGEBRA & DISCRETE MATHEMATICS

Collections

Department of Mathematics, Article

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Citation Formats

M. G. Benli, “On the condensation property of the lamplighter groups and groups of intermediate growth,” ALGEBRA & DISCRETE MATHEMATICS, pp. 222–231, 2014, Accessed: 00, 2021. [Online]. Available: http://adm.luguniv.edu.ua/.