Abstract
It is not known whether a central division algebra D of prime degree p over a field F can be noncyclic. Every such algebra which has been constructed is cyclic and, when any of various mild conditions is imposed on D, it can be proved that D is cyclic. We consider only the case in which the characteristic of D is equal to its degree p. For this case, it is known' that cyclicity of D is guaranteed by the following conditions: there is an extension field K of F such that (i) K/F has degree m with (m, p) = 1; (ii) DK is cyclic with maximal subfield W which is galois over F; (iii) K/F is cyclic. We shall prove:
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