Let 𝐾 be a number field with algebraic closure K¯, and let 𝑆 be a finite set of places of 𝐾 containing all the infinite ones. Let Γ₀ be a finitely generated subgroup of Gm(K¯), and let Γ⊂Gm(K¯) be ...

The method to divide fractions is to keep the first fraction the same, turn the divide sign into a multiply and turn the second fraction upside down. This is known as multiplying by the reciprocal.

Recent advances in theoretical physics have increasingly highlighted the pivotal role of algebraic structures in unifying particle physics with quantum gravity. These approaches leverage sophisticated ...