Abstract. In this article we improve the known uniform bound for subgroup growth of Chevalley groups G(Fp [[t]]). We introduce a new parameter, the ridgeline number v(G), and give new bounds for the subgroup growth of G(Fp [[t]]) expressed through v(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 G.
How many generators and relations does SL n(Fq [t, t −1 ]) need? In this paper we exhibit its explicit presentation with 9 generators and 44 relations.We investigate presentations of affine Kac-Moody groups over finite fields. Our goal is to derive finite presentations, independent of the field and with as few generators and relations as we can achieve. It turns out that any simply connected affine Kac-Moody group over a finite field has a presentation with at most 11 generators and 70 relations. We describe these presentations explicitly type by type. As a consequence, we derive explicit presentations of Chevalley groups G(Fq[t, t −1 ]) and explicit profinite presentations of profinite Chevalley groups G(Fq[[t]]).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.