English

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

Group Theory 2011-07-01 v2 Number Theory

Abstract

We prove that the number of immediate descendants of order p10p^10 of GpG_p is not PORC (Polynomial On Residue Classes) where GpG_p is the pp-group of order p9p^9 defined by du Sautoy's nilpotent group encoding the elliptic curve y2=x3xy^2=x^3-x. This has important implications for Higman's PORC conjecture.

Keywords

Cite

@article{arxiv.1106.5530,
  title  = {Non-PORC behaviour of a class of descendant $p$-groups},
  author = {Marcus du Sautoy and Michael Vaughan-Lee},
  journal= {arXiv preprint arXiv:1106.5530},
  year   = {2011}
}