Galois realizability of groups of orders $p^5$ and $p^6$

Details Galois realizability of groups of orders $p^5$ and $p^6$ Galois realizability of groups of orders $p^5$ and $p^6$

2012-01-12

arxiv.org/abs/1201.2594v1

Mathematics

Algebraic Geometry

Scientific paper

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 of
$18+(p-1)$ groups of order $p^5$ and $71+4(p-1)$ groups of order $p^6$ as
Galois groups over $k$. These obstructions are decomposed as products of
$p$-cyclic algebras, provided that $k$ contains certain roots of unity.

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