On the exponent of a finite group with an automorphism group of order twelve.

DOI10.1016/J.JALGEBRA.2010.09.038zbMath1229.20016OpenAlexW2074890729MaRDI QIDQ716478

P. V. Shumyatskij

Publication date: 22 September 2011

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.09.038

zbMATH Keywords

Frobenius groupsautomorphism groupsLie algebrasexponentsassociated Lie rings

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Automorphisms of abstract finite groups (20D45) Automorphism groups of groups (20F28) Representations of groups as automorphism groups of algebraic systems (20F29) Finite nilpotent groups, (p)-groups (20D15) Associated Lie structures for groups (20F40)

Related Items (10)

Rank and order of a finite group admitting a Frobenius group of automorphisms. ⋮ Lie algebras admitting a metacyclic Frobenius group of automorphisms ⋮ Automorphisms of finite \(p\)-groups admitting a partition. ⋮ Fitting height of a finite group with a Frobenius group of automorphisms. ⋮ Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. ⋮ Exponent of a finite group with a fixed-point-free four-group of automorphisms. ⋮ Exponent of a finite group with a four-group of automorphisms. ⋮ Nilpotent length of a finite group admitting a Frobenius group of automorphisms with fixed-point-free kernel. ⋮ On the nilpotency class of finite groups with a Frobenius group of automorphisms ⋮ Rank and order of a finite group admitting a Frobenius-like group of automorphisms.

Cites Work

• Powerful \(p\)-groups. I: Finite groups.
• Fixed points of Frobenius groups of automorphisms.
• Bounding the exponent of a finite group with automorphisms
• \(p\)-adic analytic groups
• Frobenius groups as groups of automorphisms
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• Nilpotency of Some Lie Algebras Associated with p-Groups
• FINITE $ p$-GROUPS ADMITTING $ p$-AUTOMORPHISMS WITH FEW FIXED POINTS
• Sur les groupes nilpotents et les anneaux de Lie
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