Subgroups of arbitrary even ordinary depth

Abstract

We show that for each positive integer $n$, there are a group $G$ and a subgroup $H$ such that the ordinary depth is $d(H, G) = 2n$. This solves the open problem posed by Lars Kadison whether even ordinary depth larger than $6$ can occur.Comment: 9 pages; the new version fixes two citations (the numbers stated in the first version referred to a non-final version of the cited paper) and adds some motivating example