Subgroups of arbitrary even ordinary depth

2019/02/01 by Hayder Abbas Janabi, Thomas Breuer, Janabi, Hayder Abbas +3
Engineering · Mathematics · #05C12 #05C76 (secondary) #20B35 #20C15 (primary) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1902.00512

openalex publication_date 2019/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the depth of subgroups of simple groups
• On subgroup depth
• The depth of a finite simple group
• Subgroups of depth three and more
• The depth of subgroups of Suzuki groups