Abstract:For rings of algebraic integers [Formula: see text] in a number field [Formula: see text] called [Formula: see text]-pseudo-good, this paper describes a bounded generation result concerning the minimal number of conjugates of suitable elementary matrices (or more precisely root elements) in [Formula: see text] needed to write any element of the [Formula: see text]-principal congruence subgroup of [Formula: see text] as their product. Using this bounded generation result, we give explicit bounds for the diamete… Show more
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.