Subgroups of arbitrary even ordinary depth

Hayder Abbas Janabi; Thomas Breuer; Erzsebet Horvath

Subgroups of arbitrary even ordinary depth

Group Theory 2020-06-19 v2 Representation Theory

Authors: Hayder Abbas Janabi , Thomas Breuer , Erzsebet Horvath

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.

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@article{arxiv.1902.00512,
  title  = {Subgroups of arbitrary even ordinary depth},
  author = {Hayder Abbas Janabi and Thomas Breuer and Erzsebet Horvath},
  journal= {arXiv preprint arXiv:1902.00512},
  year   = {2020}
}

Comments

9 pages; the new version fixes two citations (the numbers stated in the first version referred to a non-final version of the cited paper) and adds some motivating examples

Subgroups of arbitrary even ordinary depth

Abstract

Cite

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