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math.NT2025
On Variants of Inverse Cluster Size Problem & General Magnification
Shubham Jaiswal, M Krithika, P Vanchinathan
In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the proble…
math.NT2025
On Minimal generating sets of splitting field, Cluster towers and Multiple transitivity of Galois groups
Shubham Jaiswal, P Vanchinathan
A natural generating set for a Galois extension regarded as the splitting field of an irreducible polynomial is introduced and investigated here. Minimal generating sets arising in…
math.NT2025
Inflated G-Extensions for Algebraic Number Fields
M Krithika, P Vanchinathan
In 2018, Legrand and Paran proved a weaker form of the Inverse Galois Problem for all Hilbertian fields and all finite groups: that is, there exist possibly non-Galois extensions o…