Counting \(p\)-groups and nilpotent groups

DOI10.1007/BF02698914zbMath1017.20012OpenAlexW1967396882WikidataQ29036193 ScholiaQ29036193MaRDI QIDQ5945306

Marcus P. F. du Sautoy

Publication date: 7 April 2002

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_2000__92__63_0

zbMATH Keywords

finite \(p\)-groupszeta functionsdefinable \(p\)-adic integralsnumbers of points on varieties mod \(p\)PORC conjecture

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Asymptotic results on counting functions for algebraic and topological structures (11N45) Other Dirichlet series and zeta functions (11M41) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Galois trees in the graph of \(p\)-groups of maximal class ⋮ Coclass theory for nilpotent semigroups via their associated algebras. ⋮ The distribution of second \(p\)-class groups on coclass graphs ⋮ Book Review: Groups of prime power order. Vol. 1 (with a foreword by Zvonimir Janko); Groups of prime power order. Vol. 2 ⋮ Non-PORC behaviour of a class of descendant \(p\)-groups. ⋮ On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients ⋮ The origins of coclass theory ⋮ Orbit isomorphic skeleton groups ⋮ Metabelian \(p\)-groups and coclass theory. ⋮ Schur multiplicators of finite \(p\)-groups with fixed coclass. ⋮ COMPUTATION OF LOW-DIMENSIONAL (CO)HOMOLOGY GROUPS FOR INFINITE SEQUENCES OF p-GROUPS WITH FIXED COCLASS ⋮ Finite \(p\)-groups of maximal class with `large' automorphism groups ⋮ A classification of the harmonic frames up to unitary equivalence ⋮ Normal subgroup growth in free class-2-nilpotent groups. ⋮ A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups ⋮ Enumerating graded ideals in graded rings associated to free nilpotent Lie rings ⋮ Periodic patterns in the graph of p-groups of maximal class ⋮ Zeta functions enumerating normal subgroups of \(\mathfrak{T}_2\)-groups and their behavior on residue classes ⋮ Zeta functions and counting finite p-groups ⋮ Enumerating finite class-2-nilpotent groups on 2 generators. ⋮ ON THE CLASSIFICATION OF GROUPS OF PRIME-POWER ORDER BY COCLASS: THE 3-GROUPS OF COCLASS 2

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