Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 
 

 

Subgroup growth in some profinite Chevalley groups


Authors: Inna Capdeboscq, Karina Kirkina and Dmitriy Rumynin
Journal: Proc. Amer. Math. Soc. 145 (2017), 4187-4200
MSC (2010): Primary 20E07; Secondary 17B45, 17B70
DOI: https://doi.org/10.1090/proc/13567
Published electronically: April 7, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this article we improve the known uniform bound for subgroup growth of Chevalley groups $ \mathbf {G}(\mathbb{F}_p[[t]])$. We introduce a new parameter, the ridgeline number $ v(\mathbf {G})$, and give new bounds for the subgroup growth of $ \mathbf {G}(\mathbb{F}_p[[t]])$ expressed through $ v(\mathbf {G})$. We achieve this by deriving a new estimate for the codimension of $ [U,V]$ where $ U$ and $ V$ are vector subspaces in the Lie algebra of $ \mathbf {G}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20E07, 17B45, 17B70

Retrieve articles in all journals with MSC (2010): 20E07, 17B45, 17B70


Additional Information

Inna Capdeboscq
Affiliation: Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: I.Capdeboscq@warwick.ac.uk

Karina Kirkina
Affiliation: Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: K.Kirkina@warwick.ac.uk

Dmitriy Rumynin
Affiliation: Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: D.Rumynin@warwick.ac.uk

DOI: https://doi.org/10.1090/proc/13567
Keywords: Subgroup growth, Lie algebras, Chevalley groups
Received by editor(s): November 13, 2015
Received by editor(s) in revised form: August 31, 2016, October 25, 2016, and November 2, 2016
Published electronically: April 7, 2017
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society