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arXiv · 1806.10511

Enumerating isoclinism classes of semi-extraspecial groups

Mark L. Lewis·Joshua Maglione
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Abstract

We enumerate the number of isoclinism classes of semi-extraspecial $p$-groups with derived subgroup of order $p^2$. To do this, we enumerate $\text{GL}(2, p)$-orbits of sets of irreducible, monic polynomials in $\mathbb{F}_p[x]$. Along the way, we also provide a new construction of an infinite family of semi-extraspecial groups as central quotients of Heisenberg groups over local algebras.

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Mark L. Lewis, Joshua Maglione. 2018-09-12. Enumerating isoclinism classes of semi-extraspecial groups. https://doi.org/10.1017/s0013091519000531

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