Galois realizability of groups of orders p⁵ and p⁶

2012/01/12 by Ivo Michailov Michailov, Michailov, Ivo Michailov
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1201.2594

In this version I corrected the statements of the main results. The paper will appear in Central European Journal of Mathematics

arxiv created 2012/06/05 · arxiv updated 2012/06/06

Abstract

Let p be an odd prime, and let k be an arbitrary field of characteristic not p. In this article we determine the obstructions for the realizability as Galois groups over k of all groups of orders p⁵ and p⁶, that have an abelian quotient obtained by factoring out central subgroups of order p or p². These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.

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