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- Title
Bounded generation for congruence subgroups of Sp4(R).
- Authors
Trost, Alexander A.
- Abstract
For rings of algebraic integers R in a number field K called 2 R -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 Sp 4 (R) needed to write any element of the 2 R -principal congruence subgroup of Sp 4 (R) as their product. Using this bounded generation result, we give explicit bounds for the diameter of word norms on Sp 4 (R) given by conjugacy classes thereby continuing an investigation into such diameters by Kedra et al. Additionally, we present some examples of 2 R -pseudo-good rings and classify normally generating subsets of Sp 4 (R) for R the ring of algebraic integers in any number field.
- Subjects
RING theory; RINGS of integers; GEOMETRIC congruences
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501748