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

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

2011-06-27

arxiv.org/abs/1106.5530v2

Mathematics

Group Theory

Scientific paper

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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