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In 1978 Amitsur and Saltman constructed generic abelian crossed product
p-algebras containing no non-trivial p-power central elements. These algebras
are examples of noncyclic p-algebras and the existence of such algebras answered a
question of Albert. In this talk we discuss these terms and talk about why prime to
p extensions of these algebras are of interest and what is known about them.
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