The Dade group of (almost) extraspecial $p$-groups.

Bouc, Serge and Mazza, Nadia (2004) The Dade group of (almost) extraspecial $p$-groups. Journal of Pure and Applied Algebra, 192 (1-3). pp. 21-51. ISSN 0022-4049

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Abstract

In this paper, we determine a presentation by explicit generators and relations for the Dade group of all (almost) extraspecial $p$-groups. The proof of the main result uses the cohomological properties of the Tits building corresponding to the natural geometric structure of the lattice of subgroups of such $p$-groups.