Title: Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields
Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach takes the factorization of X^n-1 as the model and defines cyclotomic polynomials relative to an algebraic integer.
The methods (not the results) used were surprisingly found to solve a classical question (but asked and solved over Q only in 2004 and forgotten) over number fields. Given an irreducible polynomial over a number field how many of its roots are found in the extension obtained by adjoining a single root.
Finally we show how to find number field extensions which are poor in automorphisms -- poor in a precise technical manner having a specified inflation index and a specific group as the automorphism group.
This is a joint work with M Krithika.