Commutator endomorphisms of totally projective abelian π-groups
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Patrick Keef
Abstract
For a primary abelian group πΊ, Chekhlov and Danchev (2015) defined three variations of Kaplanskyβs notion of full transitivity by restricting oneβs attention to the subgroup, the subring and the unitary subring of the endomorphism ring of πΊ generated by the collection of all commutator endomorphisms. They posed the problem of describing exactly which totally projective groups exhibit these forms of full transitivity. This problem, and some closely related questions, are completely answered using the Ulm function of πΊ.
Acknowledgements
The author expresses his thanks to the referee who made suggestions that significantly improved the exposition in this work.
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Communicated by: John S. Wilson
References
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Articles in the same Issue
- Frontmatter
- The Higman operations and embeddings of recursive groups
- Redundant relators in cyclic presentations of groups
- Commutator endomorphisms of totally projective abelian π-groups
- Algebraic groups over finite fields: Connections between subgroups and isogenies
- Relative stable equivalences of Morita type for the principal blocks of finite groups and relative Brauer indecomposability
- 5-Regular prime graphs of finite nonsolvable groups
- On weak commutativity in π-groups
- More on chiral polytopes of type \{4, 4, β¦, 4\} with~solvable automorphism groups
Articles in the same Issue
- Frontmatter
- The Higman operations and embeddings of recursive groups
- Redundant relators in cyclic presentations of groups
- Commutator endomorphisms of totally projective abelian π-groups
- Algebraic groups over finite fields: Connections between subgroups and isogenies
- Relative stable equivalences of Morita type for the principal blocks of finite groups and relative Brauer indecomposability
- 5-Regular prime graphs of finite nonsolvable groups
- On weak commutativity in π-groups
- More on chiral polytopes of type \{4, 4, β¦, 4\} with~solvable automorphism groups
