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arXiv · 1106.5530

Non-PORC behaviour of a class of descendant $p$-groups

Marcus du Sautoy·Michael Vaughan-Lee
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Abstract

We prove that the number of immediate descendants of order $p^10$ of $G_p$ is not PORC (Polynomial On Residue Classes) where $G_p$ is the $p$-group of order $p^9$ defined by du Sautoy's nilpotent group encoding the elliptic curve $y^2=x^3-x$. This has important implications for Higman's PORC conjecture.

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Marcus du Sautoy, Michael Vaughan-Lee. 2011-06-30. Non-PORC behaviour of a class of descendant $p$-groups. https://arxiv.org/abs/1106.5530

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