The origins of coclass theory

DOI10.1007/s00013-023-01867-wzbMath1529.20027arXiv2305.05243OpenAlexW4382317899MaRDI QIDQ6139347

Heiko Dietrich, Bettina Eick

Publication date: 18 December 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.05243

zbMATH Keywords

finite \(p\)-groupspro-\(p\)-groupscoclass graphcoclass theory

Mathematics Subject Classification ID

Finite nilpotent groups, (p)-groups (20D15) Limits, profinite groups (20E18) History of group theory (20-03) Computational methods for problems pertaining to group theory (20-08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Character degrees of finite \(p\)-groups by coclass.
• Finite \(p\)-groups of maximal class with `large' automorphism groups
• Computing \(p\)-groups with trivial Schur multiplicator.
• On coclass and trivial Schur multiplicator.
• On a special class of \(p\)-groups
• Schur multiplicators of infinite pro-\(p\)-groups with finite coclass.
• Schur multiplicators of finite \(p\)-groups with fixed coclass.
• Some remarks on Sylow subgroups of general linear groups
• Space groups and groups of prime-power order. VIII: Pro-p-groups of finite coclass and p-adic Lie algebras
• Space groups and groups of prime-power order. II: Classification of space groups by finite factor groups
• Space groups and groups of prime-power order. I
• The structure of finite \(p\)-groups: Effective proof of the coclass conjectures
• Cohomology of uniserial \(p\)-adic space groups with cyclic point group
• On the Schur multipliers of finite \(p\)-groups of given coclass.
• The \(p\)-group generation algorithm
• Galois trees in the graph of \(p\)-groups of maximal class
• Nilpotent associative algebras and coclass theory.
• Coclass theory for nilpotent semigroups via their associated algebras.
• Coclass and cohomology.
• Automorphism groups of 2-groups.
• Über \(p\)-Gruppen von maximaler Klasse
• ON THE CLASSIFICATION OF GROUPS OF PRIME-POWER ORDER BY COCLASS: THE 3-GROUPS OF COCLASS 2
• On Efficient Presentations for Infinite Sequences of 2-Groups with Fixed Coclass
• COCHAIN SEQUENCES AND THE QUILLEN CATEGORY OF A COCLASS FAMILY
• COMPUTATION OF LOW-DIMENSIONAL (CO)HOMOLOGY GROUPS FOR INFINITE SEQUENCES OF p-GROUPS WITH FIXED COCLASS
• A new pattern in the graph ofp-groups of maximal class
• Periodic patterns in the graph of p-groups of maximal class
• On 3-groups of second maximal class
• Automorphisms of Solvable Groups
• ON THE CLASSIFICATION OF p-GROUPS OF MAXIMAL CLASS
• On the classification of prime-power groups by coclass
• The Metabelian p-Groups of Maximal Class. II
• Space Groups and Groups of Prime-Power Order, V. A Bound to the Dimension of Space Groups with Fixed Coclass
• ON THE STRUCTURE OF A SPECIAL CLASS OF p-GROUPS
• Space Groups and Groups of Prime-Power Order IV. Counterexamples to the Class-Breadth Conjecture
• Pro-p groups of finite coclass
• Space Groups and Groups of Prime Power order VII. Powerful p -Groups and Uncovered p -Groups
• Some p-Groups of Maximal Class
• 2-groups of almost maximal class
• ON p-GROUPS OF MAXIMAL CLASS I
• A computer aided classification of certain groups of prime power order
• The Metabelian p-Groups of Maximal Class
• ON p-GROUPS OF MAXIMAL CLASS II
• ON p-GROUPS OF MAXIMAL CLASS III
• Classifying 2-groups by coclass
• Pro-p -Groups of Finite Coclass
• The Structure of Finite p -Groups
• The Precise Bound to the Coclass of Space Groups
• A note on skeleton groups in coclass graphs
• Space Groups and Groups of Prime Power Order VI. a Bound to the Dimension of a 2-Adic Space Group with Fixed Coclass
• The Coclass of a Restricted Lie Algebra
• Coclass Theory for Finite Nilpotent Associative Algebras: Algorithms and a Periodicity Conjecture
• Rank, Coclass, and Cohomology
• DETERMINATION OF THE UNISERIAL SPACE GROUPS WITH A GIVEN COCLASS
• Sylow 𝑝-subgroups of the general linear group
• Endliche Gruppen I
• Metabelian p-Groups of Maximal Class
• On the number of infinite branches in the graph of all p-groups of coclass r
• Counting \(p\)-groups and nilpotent groups

This page was built for publication: The origins of coclass theory