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Almost simple subgroups of the space Cremona group
Abstract
We prove that every finite almost simple subgroup that is not simple of the group of birational automorphisms of the three-dimensional complex projective space is isomorphic to one of the following: S5, S6, PGL2(𝔽7) or PGL2(𝔽9). We also prove that the group of birational automorphisms of the three-dimensional complex projective space contains unique (up to conjugation) subgroups isomorphic to PGL2(𝔽7) and PGL2(𝔽9).
Related
- The derived length of subgroups of the Cremona group
- p-elementary non-cyclic subgroups of the Cremona group of the plane
- The structure and generation of the second maximal subgroups of the almost simple groups with alternating, classical or sporadic socle
- Finite Groups with Few Almost Maximal Subgroups
- Invariant random subgroups of C*-simple groups
BibTeX
@misc{fuentes2026almost,
title = {{Almost simple subgroups of the space Cremona group}},
author = {Sebastián Fuentes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31628},
eprint = {2610.31628},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31628},
}
RIS
TY - UNPB
TI - Almost simple subgroups of the space Cremona group
AU - Sebastián Fuentes
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31628
UR - https://arxiv.org/abs/2610.31628
AB - We prove that every finite almost simple subgroup that is not simple of the group of birational automorphisms of the three-dimensional complex projective space is isomorphic to one of the following: S_5, S_6, PGL_2(𝔽_7) or PGL_2(𝔽_9). We also prove that the group of birational automorphisms of the three-dimensional complex projective space contains unique (up to conjugation) subgroups isomorphic to PGL_2(𝔽_7) and PGL_2(𝔽_9).
ER -