A class of descendant \(p\)-groups of order \(p^{9}\) and Higman's PORC conjecture

DOI10.1016/j.jalgebra.2016.08.042zbMath1355.20015OpenAlexW2520491276WikidataQ122966791 ScholiaQ122966791MaRDI QIDQ324241

Seungjai Lee

Publication date: 10 October 2016

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2016.08.042

zbMATH Keywords

finite \(p\)-groupsgroup theoryHigman's PORC conjecture

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Finite nilpotent groups, (p)-groups (20D15) Varieties over finite and local fields (11G25) Associated Lie structures for groups (20F40)

Related Items (5)

Kirillov's orbit method and polynomiality of the faithful dimension of $p$-groups ⋮ Non-PORC behaviour in groups of order \(p^{7}\) ⋮ Hessian matrices, automorphisms of \(p\)-groups, and torsion points of elliptic curves ⋮ Zeta functions enumerating normal subgroups of \(\mathfrak{T}_2\)-groups and their behavior on residue classes ⋮ Some unsolvable conjectures in finite \(p\)-groups

Uses Software

• Magma

Cites Work

• The Magma algebra system. I: The user language
• The \(p\)-group generation algorithm
• Groups and nilpotent Lie rings whose order is the sixth power of a prime.
• Non-PORC behaviour of a class of descendant \(p\)-groups.
• The groups with order \(p^7\) for odd prime \(p\).
• Reciprocity laws and Galois representations: recent breakthroughs
• Higman's PORC conjecture for a family of groups
• Enumerating p -Groups, II: Problems Whose Solution is PORC
• Groups of order $p^8$ and exponent $p$
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