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On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group
Abstract
We show some sufficient conditions ( in terms of properties of A, B and X) for the non-abelian exterior square G ∧ G to be residually finite, where $G $ is the wreath product A wr B or the combinatorial wreath product G = A wrX B, in the latter case B is a free group. We prove that for the Grigorchuk group G the non-abelian exterior square G ∧ G and the non-abelian tensor product G ⊗ G are residually finite. We show conditions that imply that A wr B is not (cohomologically) good in dimension ≤ 2.
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BibTeX
@misc{teixeira2026residual,
title = {{On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group}},
author = {Ayrton Anjos Teixeira and Dessislava H. Kochloukova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10417},
eprint = {2610.10417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10417},
}
RIS
TY - UNPB
TI - On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group
AU - Ayrton Anjos Teixeira
AU - Dessislava H. Kochloukova
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10417
UR - https://arxiv.org/abs/2610.10417
AB - We show some sufficient conditions ( in terms of properties of A, B and X) for the non-abelian exterior square G ∧ G to be residually finite, where $G $ is the wreath product A wr B or the combinatorial wreath product G = A wr_X B, in the latter case B is a free group. We prove that for the Grigorchuk group G the non-abelian exterior square G ∧ G and the non-abelian tensor product G ⊗ G are residually finite. We show conditions that imply that A wr B is not (cohomologically) good in dimension ≤ 2.
ER -