Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements

DOI10.1142/S0219498819500555zbMath1481.20081arXiv1601.04311OpenAlexW2964218321MaRDI QIDQ5383829

Alexander Bors

Publication date: 20 June 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04311

zbMATH Keywords

finite groupsautomorphismssolvable radicalFitting subgrouppowers of group elements

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Extremal set theory (05D05) Finite fields (field-theoretic aspects) (12E20) Automorphisms of abstract finite groups (20D45) Finite simple groups and their classification (20D05)

Related Items (3)

Fibers of word maps and the multiplicities of non-abelian composition factors ⋮ Groups satisfying identities with high probability ⋮ Worst-case approximability of functions on finite groups by endomorphisms and affine maps

Cites Work

• Unnamed Item
• On the number of characters in a \(p\)-block of a \(p\)-solvable group
• Nonsolvable groups with an automorphism inverting many elements
• Upper bounds for the number of conjugacy classes of a finite group
• On a conjecture of Zimmerman about group automorphisms
• Finite groups admitting a fixed-point-free automorphism group
• Isoclinism classes and commutativity degrees of finite groups
• Finite groups with an automorphism of large order
• On the commuting probability in finite groups.
• The number of conjugacy classes in a finite group
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements
• Reversibility in Dynamics and Group Theory
• Soluble Groups with an Automorphism Inverting Many Elements
• FINITE GROUPS WITH AN AUTOMORPHISM CUBING A LARGE FRACTION OF ELEMENTS
• ON AUTOMORPHISMS OF FINITE GROUPS
• Automorphism Groups of Groups with Trivial Centre
• What is the Probability that Two Group Elements Commute?
• Groups with an automorphism cubing many elements
• Groups with an automorphism squaring many elements

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