Subgroups of arbitrary even ordinary depth

Abstract

‎We show that for each positive integer $n$‎, ‎there exist a group $G$ and a subgroup $H$ such that the ordinary depth $d(H‎, ‎G)$ is $2n$‎. ‎This solves the open problem posed by Lars Kadison whether even ordinary depth larger than $6$ can occur‎.

Keywords

• ‎ordinary depth of a subgroup‎
• ‎distance of characters‎
• ‎cartesian product of graphs‎
• ‎wreath product