Let D D be a division algebra of prime degree p p . A set of criteria is given for cyclicity of D D in terms of subgroups of the multiplicative group D ∗ D^* of D D . It is essentially shown that D D is cyclic if and only if D ∗ D^* contains a nonabelian metabelian subgroup.
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Mahdavi-Hezavehi et al. (2003) studied this question.
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