PreprintCC BY 4.0arXiv
Redundant generation in PSL2(ℚp)
Abstract
Given a free group on n generators, Fn, and a topological group G, Aut(Fn) acts on Epi(Fn,G), the set of homomorphisms f:Fn → G with dense image. f∈ Epi(Fn,G) is called redundant if there is a proper free factor A < Fn whose image under f is dense in G. For n ≥ 3, G = PSL2 (ℚp), we prove that every f∈ Epi(Fn,G) with torsion-free image is redundant, and give sufficient conditions for f to be redundant even when its image is not torsion-free.
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BibTeX
@misc{glasner2026redundant,
title = {{Redundant generation in $\operatornamePSL_2\left(\mathbbQ_p\right)$}},
author = {Yair Glasner and Amit Levinson-Sela},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37237},
eprint = {2609.37237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37237},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Redundant generation in PSL_2(ℚ_p)
AU - Yair Glasner
AU - Amit Levinson-Sela
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37237
UR - https://arxiv.org/abs/2609.37237
AB - Given a free group on n generators, F_n, and a topological group G, Aut(F_n) acts on Epi(F_n,G), the set of homomorphisms f:F_n → G with dense image. f∈ Epi(F_n,G) is called redundant if there is a proper free factor A < F_n whose image under f is dense in G. For n ≥ 3, G = PSL_2 (ℚ_p), we prove that every f∈ Epi(F_n,G) with torsion-free image is redundant, and give sufficient conditions for f to be redundant even when its image is not torsion-free.
ER -