Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Maximal Haagerup subgroups in $\mathbb{Z}^{n+1}\rtimes_{ρ_n}GL_2(\mathbb{Z})$ (2303.06450v3)

Published 11 Mar 2023 in math.GR and math.RT

Abstract: For $n\geq 1$, let $\rho_n$ denote the standard action of $GL_2(\Z)$ on the space $P_n(\Z)\simeq\Z{n+1}$ of homogeneous polynomials of degree $n$ in two variables, with integer coefficients. For $G$ a non-amenable subgroup of $GL_2(\Z)$, we describe the maximal Haagerup subgroups of the semi-direct product $\Z{n+1}\rtimes_{\rho_n} G$, extending the classification of Jiang-Skalski \cite{JiSk} of the maximal Haagerup subgroups in $\Z2\rtimes SL_2(\Z)$. We prove that, for $n$ odd, the group $P_n(\Z)\rtimes SL_2(\Z)$ admits infinitely many pairwise non-conjugate maximal Haagerup subgroups which are 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 which are isomorphic to $SL_2(\Z)$.

Summary

We haven't generated a summary for this paper yet.