Powerful \(p\)-groups have non-inner automorphisms of order \(p\) and some cohomology.

DOI10.1016/j.jalgebra.2009.10.013zbMath1193.20024arXiv0901.3182OpenAlexW2963212856WikidataQ56094143 ScholiaQ56094143MaRDI QIDQ2270124

Alireza Abdollahi

Publication date: 12 March 2010

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

Full work available at URL: https://arxiv.org/abs/0901.3182

zbMATH Keywords

finite \(p\)-groupsTate cohomologypowerful \(p\)-groups\(p\)-central groupsnon-inner automorphismsautomorphisms of \(p\)-groups

Mathematics Subject Classification ID

Cohomology of groups (20J06) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15)

Related Items (20)

ON NONINNER 2-AUTOMORPHISMS OF FINITE 2-GROUPS ⋮ NONINNER AUTOMORPHISMS OF ORDER IN FINITE -GROUPS OF COCLASS 2, WHEN ⋮ On noninner automorphisms of finite p-groups that fix the Frattini subgroup elementwise ⋮ Non-inner automorphisms of order \(p\) in finite \(p\)-groups of coclass 3 ⋮ Discrete valuation rings, partitions and \(p\)-groups. I ⋮ Finite \(p\)-groups of class 3 have noninner automorphisms of order \(p\). ⋮ Cohomologically trivial modules over finite groups of prime power order. ⋮ Noninner automorphisms of order \(p\) in some finite \(p\)-groups ⋮ Noninner automorphisms of order \(p\) for finite \(p\)-groups of restricted coclass ⋮ A NOTE ON AUTOMORPHISMS OF FINITE p-GROUPS ⋮ ON NONINNER AUTOMORPHISMS OF FINITE NONABELIAN -GROUPS ⋮ EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER p IN SOME FINITE p-GROUPS ⋮ ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS ⋮ A NOTE ON p-CENTRAL GROUPS ⋮ SOME PROPERTIES OF SEMI-ABELIAN -GROUPS ⋮ On noninner automorphisms of finite $p$-groups that fix the center elementwise ⋮ Finite $2$-groups of class $2$ with a specific automorphism group ⋮ On noninner automorphisms of 2-generator finite p-groups ⋮ A note on the existence of noninner automorphisms of order p in some finite p-groups ⋮ Some unsolvable conjectures in finite \(p\)-groups

Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
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• Noninner automorphisms of order \(p\) of finite \(p\)-groups
• Some remarks on groups in which elements with the same \(p\)-power commute
• Finite \(p\)-groups of class 2 have noninner automorphisms of order \(p\).
• Nichtabelsche p-Gruppen besitzen äußere p-Automorphismen
• Cohomological topics in group theory.
• Metacyclic groups
• Outer Automorphisms in Nilpotent p -Groups of Class 2
• Presentations of metacyclic groups

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