By R. Göbel, L. Lady, A. Mader
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Extra resources for Abelian Group Theory. Proc. conf. Honolulu, 1983
A:,,) coeﬁicients of coefficients can be expressed polynomials. equation an can be found always form of the (z h(ma(1)ama(2)a >ma(n))) (3 h("I7lam2> `\x95& 0) ‘H: _ _ - in polynomials as elementary symmetric polyﬁnd a simple equation for which whose such solu- in the the symmetric elementary construction solutions equations for given polynomial h(:z:1,$2, a one solution a the sys- for methods search to sense is, from how expressible are the was values intermediate be determined can . recognized Lagrange Via is .
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Formulas Solution Additional - ‘ - - the from among product is formed from a suitable selection that n! permuations, 1,2,. is, exchanges of the Variables’ indices chosen such that 0 are every possible Concretely, the permutations the from can arise that permuting through ,:rn) h(:E1, polynomial in the product. variables Then, as exactly once ,a;,, appears 931, achieves that the coeﬂicients of the equation arising shall see, one We the where . . for . . unknown the . z be can calculated in terms of the coefficients of general equations, that is, the elementary symmetric polynomiTherefore, for the polynomial operations.