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

2014-06-01
Benli, Mustafa Gökhan
Rostislav, Grigorchuk
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.
Citation Formats
M. G. Benli and G. Rostislav, “On the condensation property of the lamplighter groups and groups of intermediate growth,” pp. 222–231, 2014, Accessed: 00, 2021. [Online]. Available: http://adm.luguniv.edu.ua/.