Dihedral Quintic Fields with a Power Basis

It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p

On the Common Index Divisors of a Dihedral Field of Prime Degree

A criterion for a prime to be a common index divisor of a dihedral field of prime degree is given. This criterion is used to determine the index of families of dihedral fields of degrees 5 and 7

Families of non-congruent numbers with arbitrarily many prime factors

AbstractA method is given for generating families of non-congruent numbers with arbitrarily many prime factors. We then use this method to construct an infinite set of new families of these numbers with prime factors of the form 8k+3

INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D₅

We give an infinite family of intersective polynomials with Galois group D5, the dihedral group of order 10

Topics in homomorphisms in representation theory of symmetric groups

Bibliography: p. 213-214

Modular representations of the alternating groups

Bibliography: p. 115

The 2-Power Degree Subfields of the Splitting Fields of Polynomials with Frobenius Galois Groups

Let f(x) be an irreducible polynomial of odd degree n > 1 whose Galois group is a Frobenius group. We suppose that the Frobenius complement is a cyclic group of even order h. Let 2t h. For each i = 1, 2,..., t we show that the splitting field L of f(x) has exactly one subfield Ki with [Ki : ℚ] = 2i. These subfields form a tower of normal extensions ℚ ⊂ K1 ⊂ K2 ⊂ .... ⊂ Kt with [Ki : Ki-1] = 2 (i = 1, 2,..,t) and K0 = ℚ. Our main result in this paper is an explicit formula for an element αi in Ki-1 such that K i = ℚ(√αi) (i = 1, 2,..., t). This result is applied to DeMoivre's quintic x5 - 5ax3 + 5a2x - b, solvable quintic trinomials x5 + ax + b, as well as to some numerical polynomials of degrees 5, 9, and 13