On the finite index subgroups of Houghton's groups

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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!


  • math.GR


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