Subgroups of arbitrary even ordinary depth

Document Type : Research Paper

Authors

1 Department of Algebra, Budapest University of Technology and Economics, H-1111 Budapest, M˝ uegyetem rkp. 3–9, Hungary

2 Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14-16, D-52062 Aachen, German

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.

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Main Subjects


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