University of Isfahan International Journal of Group Theory 2251-7650 10 4 2021 12 01 Subgroups of arbitrary even ordinary depth 159 166 24854 10.22108/ijgt.2020.123551.1628 EN Hayder Janabi Department of Algebra, Budapest University of Technology and Economics, H-1111 Budapest, M˝ uegyetem rkp. 3–9, Hungary Thomas Breuer Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14-16, D-52062 Aachen, German Erzsébet Horváth Department of Algebra, Budapest University of Technology and Economics, H-1111 Budapest, M˝ uegyetem rkp. 3–9, Hungary Journal Article 2020 06 16 ‎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. ‎ordinary depth of a subgroup‎ ‎distance of characters‎ ‎Cartesian product of graphs‎ ‎wreath product https://ijgt.ui.ac.ir/article_24854_1820d1f77af97a34533fdbcf1967c68f.pdf