On the finite index subgroups of Houghton's groups

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Houghton's groups $H_2, H_3, \ldots$ have been studied in many contexts, and various results exist for their finite index subgroups. In this note we describe all of the finite index subgroups of each Houghton group, and their isomorphism types. Using the standard notation that $d(G)$ denotes the minimal size of generating set for $G$ we then show, for each $n\in \{2, 3,\ldots\}$ and $U$ of finite index in $H_n$, that $d(U)\in\{d(H_n), d(H_n)+1\}$ and characterise when each of these cases occurs.
Original languageEnglish
JournalArchiv der Mathematik
Publication statusAccepted/In press - 15 Jul 2021

Bibliographical note

6 pages; comments welcome!

Keywords

  • math.GR

Fingerprint

Dive into the research topics of 'On the finite index subgroups of Houghton's groups'. Together they form a unique fingerprint.

Cite this