English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For $n\geq 1$, let $\rho_n$ denote the standard action of $GL_2(\Z)$ on thespace $P_n(\Z)\simeq\Z^{n+1}$ of homogeneous polynomials of degree $n$ in twovariables, with integer coefficients. For $G$ a non-amenable subgroup of$GL_2(\Z)$, we describe the maximal Haagerup subgroups of the semi-directproduct $\Z^{n+1}\rtimes_{\rho_n} G$, extending the classification ofJiang-Skalski \cite{JiSk} of the maximal Haagerup subgroups in $\Z^2\rtimesSL_2(\Z)$. We prove that, for $n$ odd, the group $P_n(\Z)\rtimes SL_2(\Z)$admits infinitely many pairwise non-conjugate maximal Haagerup subgroups whichare free groups; and that, for $n$ even, the group $P_n(\Z)\rtimes GL_2(\Z)$admits infinitely many pairwise non-conjugate maximal Haagerup subgroups whichare isomorphic to $SL_2(\Z)$.

Maximal Haagerup subgroups in $\mathbb{Z}^{n+1}\rtimes_{\rho_n}GL_2(\mathbb{Z})$