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

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• 作者：Marcus du Sautoy ^{dusautoy@maths.ox.ac.uk} ; Michael Vaughan-Lee ; ¹ ; ^{michael.vaughan-lee@chch.ox.ac.uk}
• 关键词：20D15 ; 11G20
• 刊名：Journal of Algebra
• 出版年：2012
• 出版时间：1 July, 2012
• 年：2012
• 卷：361
• 期：Complete
• 页码：287-312
• 全文大小：284 K

文摘

We prove that the function enumerating the number of immediate descendants of order of is not PORC (Polynomial On Residue Classes), where is the p-group of order defined by du Sautoy?s nilpotent group encoding the elliptic curve . This has important implications for Higman?s PORC conjecture.