Power Integral Bases For The Cyclotomic Field Q(ξ₂₄)

Let Qbe a rational number field, its Galois extension is K and its Galois group is Gal(K/Q), for [K:Q]=n.There is a power basis in a Galois number field K, if its ring of integers is of the form Z[a] for some α∈L.In this case a is called a generator of power basis in Galois number fields. Let αandβ be two different generators of two power bases in Galois number fields, αandβare called equivalent if β=m±σ(α) for some m∈Z and σ∈Gal(L/Q).In this paper, we give the determination of the generators of power bases in the cyclotomic field Q(ζ24). The cyclotomic integer ring of the cyclotomic fieldQ(ζ24) is Z[ζ24], soζ24is a generator of power bases in the cyclotomic fieldQ(ζ24).Sc under this condition are presented all generators of power bases in the cyclotomic field Q(ζ24).