The automorphism group of a finite \(p\)-group is almost always a \(p\)-group.

DOI10.1016/j.jalgebra.2007.01.008zbMath1120.20025arXivmath/0602039OpenAlexW2029342689WikidataQ55393277 ScholiaQ55393277MaRDI QIDQ2370216

Geir T. Helleloid, Ursula Martin Webb

Publication date: 22 June 2007

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

Full work available at URL: https://arxiv.org/abs/math/0602039

zbMATH Keywords

finite \(p\)-groupsautomorphism groupsnumbers of generatorsFrattini subgrouplower \(p\)-lengthslower central \(p\)-series

Mathematics Subject Classification ID

Automorphisms of abstract finite groups (20D45) Automorphism groups of groups (20F28) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Generating uniform random vectors in \(\mathbb Z^k_p\): the general case, The number of automorphisms of a monolithic finite group., Cohen-Lenstra moments for some nonabelian groups, Purely (non-)strongly real Beauville groups, Automorphism groups of 2-groups of coclass at most 3, Maximal linear groups induced on the Frattini quotient of a \(p\)-group, Most small \(p\)-groups have an automorphism of order 2

Uses Software

• GAP
• Cayley

Cites Work

• Three problems in combinatorial asymptotics
• The occurrence of groups as automorphisms of nilpotent p-groups
• \(p\)-nilpotence, classifying space indecomposability, and other properties of almost all finite groups
• The \(p\)-group generation algorithm
• The automorphism group of the wreath product of finite groups
• Subgroup growth.
• Automorphisms of certain unipotent groups
• Über Automorphismengruppen endlicher \(p\)-Gruppen
• The automorphism group of an extraspecial \(p\)-group
• Enumerating p -Groups. I: Inequalities
• Almost all 𝑝-groups have automorphism group a 𝑝-group
• Lie Representations and Groups of Prime Power Order
• CONSTRUCTING AUTOMORPHISM GROUPS OF p-GROUPS
• A Contribution to the Theory of Groups of Prime-Power Order
• A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS
• Enumerating p -Groups
• Varieties of groups
• On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions
• Sur les groupes nilpotents et les anneaux de Lie
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