2000 character limit reached
Profinite rigidity of affine Coxeter groups
Published 22 Apr 2024 in math.GR | (2404.14255v1)
Abstract: We prove that affine Coxeter groups are profinitely rigid.
- Determining Fuchsian groups by their finite quotients. Israel J. Math., 214(1):1–41, 2016. 10.1007/s11856-016-1341-6.
- On the profinite rigidity of triangle groups. Bull. Lond. Math. Soc., 53(6):1849–1862, 2021. 10.1112/blms.12546.
- Robert C. Brigham. On the isomorphism problem for just-infinite groups. Communications on pure and applied mathematics, XXIV:789–796, 1971.
- Absolute profinite rigidity, direct products, and finite presentability, 2023. arXiv:2312.06058.
- Higman-Thompson groups and profinite properties of right-angled Coxeter groups, 2023. arXiv:2309.06213 [math.GR].
- C. W. Curtis and I. Reiner. Representation Theory of finite groups and associative algebras, volume 11 of Pure and Applied Mathematics. Interscience Publishers, New Yourk, 1962.
- Michael W. Davis. The geometry and topology of Coxeter groups, volume 32 of London Mathematical Society Monographs. Princeton University Press, 2008.
- Profinite completions and isomorphic finite quotients. Journal of Pure and Applied Algebra, 23:227–231, 1982.
- Walter Feit. Integral representations of Weyl groups rationally equivalent to the reflection representation. J. Group Theory, 1(3):213–218, 1998. 10.1515/jgth.1998.013.
- Space groups and groups of prime-power order. II. Classification of space groups by finite factor groups. Arch. Math. (Basel), 35(3):203–209, 1980. 10.1007/BF01235339.
- Conjugacy in polycyclic groups. Comm. Algebra, 6(8):775–798, 1978. 10.1080/00927877808822268.
- Genus for groups. J. Algebra, 326:130–168, 2011. 10.1016/j.jalgebra.2010.05.018.
- Richard Kane. Reflection groups and invariant theory, volume 5 of CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer-Verlag, New York, 2001. 10.1007/978-1-4757-3542-0.
- Torsion in profinite completions. J. Pure Appl. Algebra, 88(1-3):143–154, 1993. 10.1016/0022-4049(93)90018-O.
- George Maxwell. The normal subgroups of finite and affine Coxeter groups. Proc. London Math. Soc. (3), 76(2):359–382, 1998. 10.1112/S0024611598000112.
- On quotients of Coxeter groups. J. Algebra, 639:516–531, 2024. 10.1016/j.jalgebra.2023.09.048.
- Distinguishing crystallographic groups by their finite quotients. J. Algebra, 565:548–563, 2021. 10.1016/j.jalgebra.2020.06.033.
- Narrow normal subgroups of Coxeter groups and of automorphism groups of coxeter groups. Journal of Group theory, 27:255–274, 2024.
- Alan W. Reid. Profinite rigidity. In Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. II. Invited lectures, pages 1193–1216. World Sci. Publ., Hackensack, NJ, 2018.
- The galaxy of Coxeter groups, 2022. arXiv:2211.17038 [math.GR], arXiv:2211.17038 [math.GR].
- Fibered orbifolds and crystallographic groups. Algebr. Geom. Topol., 10(3):1627–1664, 2010. 10.2140/agt.2010.10.1627.
- I. Schur. Neuer beweis eines satzes über endliche gruppen. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, pages 1013–1019, 1902.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.