Groups of order $p^5$ and their unramified Brauer groups

preprint2012arXivOpen access

We classify all groups of order $p^5$ with non-trivial unramified Brauer groups. We show that if $p>3$ , then there are precisely $\gcd (p-1,4)+\gcd (p-1,3)+1$ such groups.

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Groups of order $p^5$ and their unramified Brauer groups

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Groups of order p5p^5p5 and their unramified Brauer groups

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Groups of order $p^5$ and their unramified Brauer groups