On the Shunkov groups acting freely on Abelian groups.
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Publication:359347
DOI10.1134/S0037446613010187zbMath1295.20039MaRDI QIDQ359347
Publication date: 12 August 2013
Published in: Siberian Mathematical Journal (Search for Journal in Brave)
finite subgroupsregular automorphismslocally finite groupselements of finite ordernearfieldsShunkov groupsneardomainsperiodic partssharply 2-transitive groups
Periodic groups; locally finite groups (20F50) Automorphism groups of groups (20F28) Local properties of groups (20E25) Near-fields (12K05) Multiply transitive infinite groups (20B22)
Related Items (8)
\textit{KT}-fields and sharply triply transitive groups ⋮ Sharply 3-transitive Groups with Finite Element ⋮ On groups with involutions saturated by finite Frobenius groups ⋮ On sharply 2-transitive groups with generalized finite elements ⋮ Local finiteness of periodic sharply triply transitive groups. ⋮ Unnamed Item ⋮ On periodic groups saturated with finite Frobenius groups ⋮ Groups saturated with finite Frobenius groups
Cites Work
- Periodic groups generated by a pair of virtually quadratic automorphisms of an Abelian group.
- Periodic groups acting freely on Abelian groups.
- Fixed-point-free 2-finite automorphism groups.
- The set of elements of finite order in a biprimitively finite group
- Doubly-transitive permutation groups
- A nonsimplicity criterion for groups
- On regular automorphisms of order \(3\) and Frobenius pairs
- A new proof of Zassenhaus theorem on finite groups of fixed-point-free automorphisms
- On the structure of the noninvariant factor in some Frobenius groups
- On a class of \(p\)-groups
- ON A GENERALIZATION OF FROBENIUS' THEOREM TO INFINITE GROUPS
- A group with H-Frobenius element of even order
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