20Exx Structure and classification of groups
This subtopic studies structure and classification of groups, especially decompositions, composition series, and structural invariants that organize group theory.
Specific topics
20E05 Free nonabelian groups
Overview
20E05 studies free nonabelian groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for free nonabelian 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E06 Free products of groups, free products with amalgamation, HNN extensions
Overview
20E06 studies free products of groups, free products with amalgamation, hnn extensions in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for free products of groups, free products with amalgamation, hnn extensions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E07 Subgroup theorems; subgroup growth
Overview
20E07 studies subgroup theorems; subgroup growth in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for subgroup theorems; subgroup growth
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E08 Groups acting on trees
Overview
20E08 studies groups acting on trees in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for groups acting on trees
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E10 Quasivarieties and varieties of groups
Overview
20E10 studies quasivarieties and varieties of groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for quasivarieties and varieties of 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E15 Chains and lattices of subgroups, subnormal subgroups
Overview
20E15 studies chains and lattices of subgroups, subnormal subgroups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for chains and lattices of subgroups, subnormal subgroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E18 Limits, profinite groups
Overview
20E18 studies limits, profinite groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for limits, profinite 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E22 Extensions, wreath products, and other compositions of groups
Overview
20E22 studies extensions, wreath products, and other compositions of groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for extensions, wreath products, and other compositions of 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E25 Local properties of groups
Overview
20E25 studies local properties of groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local properties of 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E26 Residual properties and generalizations; residually finite groups
Overview
20E26 studies residual properties and generalizations; residually finite groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for residual properties and generalizations; residually finite 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E28 Maximal subgroups
Overview
20E28 studies maximal subgroups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for maximal subgroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E32 Simple groups
Overview
20E32 studies simple groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for simple 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E34 General structure theorems for groups
Overview
20E34 studies general structure theorems for groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general structure theorems for 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E36 Automorphisms of infinite groups
Overview
20E36 studies automorphisms of infinite groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphisms of infinite 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E42 Groups with a $BN$-pair; buildings
Overview
20E42 studies groups with a $bn$-pair; buildings in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for groups with a $bn$-pair; buildings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks
20E45 Conjugacy classes for groups
Overview
20E45 studies conjugacy classes for groups in structure and classification of groups. It focuses on structural theorems and classification tools that organize groups by normality, composition, and action.
Related Wikipedia Page
Structure And Classification Of Groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for conjugacy classes for 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 classify groups and compare structural regimes across finite and infinite cases.
Applications
- Structure theorems
- Classification by normal and quotient data
- Profinite and extension-based methods
References
Recommended Textbooks