20Kxx Abelian groups
This subtopic studies abelian groups, focusing on classification, torsion phenomena, and module-theoretic viewpoints.
Specific topics
20K01 Finite abelian groups
Overview
20K01 studies finite abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for finite abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K10 Torsion groups, primary groups and generalized primary groups
Overview
20K10 studies torsion groups, primary groups and generalized primary groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for torsion groups, primary groups and generalized primary groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K15 Torsion-free groups, finite rank
Overview
20K15 studies torsion-free groups, finite rank in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for torsion-free groups, finite rank
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K20 Torsion-free groups, infinite rank
Overview
20K20 studies torsion-free groups, infinite rank in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for torsion-free groups, infinite rank
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K21 Mixed groups
Overview
20K21 studies mixed groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for mixed groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K25 Direct sums, direct products, etc. for abelian groups
Overview
20K25 studies direct sums, direct products, etc. for abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for direct sums, direct products, etc. for abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K27 Subgroups of abelian groups
Overview
20K27 studies subgroups of abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for subgroups of abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
Overview
20K30 studies automorphisms, homomorphisms, endomorphisms, etc. for abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K35 Extensions of abelian groups
Overview
20K35 studies extensions of abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for extensions of abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K40 Homological and categorical methods for abelian groups
Overview
20K40 studies homological and categorical methods for abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for homological and categorical methods for abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks
20K45 Topological methods for abelian groups
Overview
20K45 studies topological methods for abelian groups in abelian groups. It studies the classification, structure, and homological properties of abelian groups across finite, torsion, and infinite-rank settings.
Related Wikipedia Page
Abelian Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topological methods for abelian groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze module-like decompositions and invariants in abelian group theory.
Applications
- Classification and decomposition
- Torsion and torsion-free structure
- Homological and topological methods
References
Recommended Textbooks