Subgroups of arbitrary even ordinary depth

DOAJ (DOAJ: Directory of Open Access Journals)

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.

Authors 2

1. Hayder Abbas Janabi

   Budapest University of Technology and Economics

   Affiliation as printed

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

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

2. Thomas G. K. Breuer Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

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