Extend the kronecker–weber theorem on abelian extensions of the rational numbers to any base number field

Description: This problem asks to extend the Kronecker-Weber Theorem on abelian extensions of the rational numbers to any base number field. The current Kronecker-Weber Theorem does this for the case of any imaginary quadratic field, showing that every algebraic integer whose Galois group is abelian can be expressed as a sum of roots of unity with rational coefficients.

Source: Wikipedia

Status: The work done by Shimura and Taniyama in the complex multiplication of abelian varieties gave rise to abelian extensions of CM-fields. Additionally, Stark’s conjecture resulted in a great conjectural development of L-functions, and is capable of producing concrete, numerical results. However, this problem still remains unresolved.

Hope this helped!!!

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐

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