PreprintCC BY 4.0arXiv
On symmetric and twisted-unitary modular units in group rings
Abstract
We study units in group rings of the Hantzsche-Wendt group. We construct a compatible system of non-trivial unitary units over ℤ/2nℤ for every n≥1, and ``almost-group'' units over ℤ/2ℤ, meaning non-trivial units u with the property that u−g=u−1−g−1 for some group element g.
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BibTeX
@misc{bartholdi2026symmetric,
title = {{On symmetric and twisted-unitary modular units in group rings}},
author = {Laurent Bartholdi and Iuliya Beloshapka and Roman Mikhailov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29273},
eprint = {2609.29273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29273},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On symmetric and twisted-unitary modular units in group rings
AU - Laurent Bartholdi
AU - Iuliya Beloshapka
AU - Roman Mikhailov
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29273
UR - https://arxiv.org/abs/2609.29273
AB - We study units in group rings of the Hantzsche-Wendt group. We construct a compatible system of non-trivial unitary units over ℤ/2^nℤ for every n≥1, and ``almost-group'' units over ℤ/2ℤ, meaning non-trivial units u with the property that u−g=u^−1−g^−1 for some group element g.
ER -