Non-PORC behaviour of a class of descendant \(p\)-groups.

DOI10.1016/j.jalgebra.2012.03.038zbMath1267.20025arXiv1106.5530OpenAlexW2964035039MaRDI QIDQ1931696

Marcus P. F. du Sautoy, Michael Vaughan-Lee

Publication date: 15 January 2013

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5530

zbMATH Keywords

finite \(p\)-groupsPORC conjecturegroup enumerationnumbers of groupslower exponent-\(p\) central seriesimmediate descendants

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Curves over finite and local fields (11G20) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Groups of order $p^8$ and exponent $p$ ⋮ A class of descendant \(p\)-groups of order \(p^{9}\) and Higman's PORC conjecture ⋮ Computational group theory. Abstracts from the workshop held August 15--21, 2021 (hybrid meeting) ⋮ Non-PORC behaviour in groups of order \(p^{7}\) ⋮ Hessian matrices, automorphisms of \(p\)-groups, and torsion points of elliptic curves ⋮ Counting Schur rings over cyclic groups ⋮ Zeta functions enumerating normal subgroups of \(\mathfrak{T}_2\)-groups and their behavior on residue classes ⋮ Some unsolvable conjectures in finite \(p\)-groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Subgroups of finite index in nilpotent groups
• The \(p\)-group generation algorithm
• Groups and nilpotent Lie rings whose order is the sixth power of a prime.
• The groups with order \(p^7\) for odd prime \(p\).
• Higman's PORC conjecture for a family of groups
• Zeta functions and counting finite p-groups
• Counting subgroups in nilpotent groups and points on elliptic curves
• Analytic properties of Euler products of Igusa-type zeta functions and subgroup growth of nilpotent groups
• Über die Anzahl der Primzahlen eines reellquadratischen Zahlkörpers, deren Konjugierte unterhalb gegebener Grenzen liegen
• Enumerating p -Groups, II: Problems Whose Solution is PORC
• Analytic properties of zeta functions and subgroup growth
• Counting \(p\)-groups and nilpotent groups