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The norm principle for extended Clifford groups
Abstract
We prove the norm principle for the extended Clifford group Ω(q) of every nondegenerate quadratic form q of even dimension at least $4$ over an arbitrary field F of characteristic different from $2$, for all finite separable field extensions L/F. The main new ingredient is a factorization theorem for proper similitudes: for a quadratic extension L/F and f∈ GO+(q)(L), there exist u∈ SO(q)(L), a maximal F-torus S⊂ GO+(q), and s∈ S(L) such that f=us.
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BibTeX
@misc{scavia2026norm,
title = {{The norm principle for extended Clifford groups}},
author = {Federico Scavia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30607},
eprint = {2609.30607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30607},
}
RIS
TY - UNPB
TI - The norm principle for extended Clifford groups
AU - Federico Scavia
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30607
UR - https://arxiv.org/abs/2609.30607
AB - We prove the norm principle for the extended Clifford group Ω(q) of every nondegenerate quadratic form q of even dimension at least $4$ over an arbitrary field F of characteristic different from $2$, for all finite separable field extensions L/F. The main new ingredient is a factorization theorem for proper similitudes: for a quadratic extension L/F and f∈ GO^+(q)(L), there exist u∈ SO(q)(L), a maximal F-torus S⊂ GO^+(q), and s∈ S(L) such that f=us.
ER -