On presentations of integer polynomial points of simple groups over number fields
Amir Mohammadi, Kevin Wortman

TL;DR
This paper investigates the algebraic structure of integer polynomial points of simple algebraic groups over number fields, showing that certain groups are not finitely presented when the K-rank is 2.
Contribution
It establishes a new non-finite presentation result for integer polynomial points of simple algebraic groups over number fields when the K-rank equals 2.
Findings
G(A[t]) is not finitely presented for K-rank 2 groups
Provides insights into the algebraic structure of polynomial points over number fields
Advances understanding of the finiteness properties of algebraic groups over rings
Abstract
Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Finite Group Theory Research · Advanced Algebra and Geometry
