# Category:Terminology local to the wiki

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This page lists terminology that is local to this wiki. For using this terminology outside the wiki, please define it appropriately.

Some of the terminology may be similar to standard terminology in related areas, and may be inspired through close parallels. In fact, in most cases, the terminology is fairly self-evident once one knows the meaning.

Learn more about terminology local to the wiki

## Pages in category "Terminology local to the wiki"

The following 200 pages are in this category, out of 590 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### 1

### A

- Abelian direct factor
- Abelian hereditarily normal subgroup
- Abelian-extensible automorphism
- Abelian-extensible automorphism-invariant subgroup
- Abelian-extensible endomorphism
- Abelian-extensible endomorphism-invariant subgroup
- Abelian-potentially characteristic subgroup
- Abelian-potentially verbal subgroup
- Abelian-quotient-pullbackable automorphism-invariant subgroup
- Absolutely normal subgroup
- Action-isomorph-free subgroup
- ACU-closed group property
- ACU-closed subgroup property
- AEP-subgroup
- Amalgam-characteristic subgroup
- Amalgam-normal-subhomomorph-containing subgroup
- Amalgam-strictly characteristic subgroup
- APS homomorphism
- APS of groups
- Associated direct sum of a subnormal series
- Asymptotically fixed-depth join-transitively subnormal subgroup
- Auto-invariance property
- Autoclinism-invariant subgroup
- Automorph-commensurable subgroup
- Automorph-conjugate subgroup
- Automorph-dominating subgroup
- Automorph-join-closed subnormal subgroup
- Automorph-permutable subgroup
- Automorphic subgroups
- Automorphically endomorph-dominating subgroup
- Automorphism-faithful subgroup

### B

- Baer alternating loop ring
- Baer diassociative loop
- Baer Lie group
- Baer Lie ring
- Baer Malcev ring
- Balanced subgroup property (function restriction formalism)
- Balanced subgroup property (generic notion)
- Base diagonal of a wreath product
- Base of a wreath product with diagonal action
- Binilpotency
- Bound-word subgroup
- Bounded-nilpotent IAPS
- Bounded-solvable IAPS

### C

- Canonically Lazard-dividable Lie ring
- Canonically Lazard-divided Lie ring
- CDIN-subgroup
- Center-fixing automorphism-balanced subgroup
- Central factor of normalizer
- Central factor-extensible automorphism
- Centralizer-annihilating endomorphism-invariant subgroup
- Centralizer-dense subgroup
- Centralizer-free subgroup
- Centralizer-large subgroup
- Chain-extensible automorphism
- Character-conjugate conjugacy classes
- Characteristic AEP-subgroup
- Characteristic subgroup of direct factor
- Characteristic subgroup-closed group property
- Characteristic transitively normal subgroup
- Characteristic-extensible automorphism
- Characteristic-isomorph-free subgroup
- Characteristic-potentially characteristic subgroup
- Characteristic-semidirectly extensible automorphism
- Characteristically complemented normal subgroup
- Characteristically complemented subgroup
- Characteristically DP-decomposable subgroup
- Characteristically Hopfian group
- Characteristically metacyclic group
- Characteristically metacylic group
- Characteristically polycyclic group
- Class two Lie cring
- Class two near-Lie cring
- Class-inner automorphism
- Class-separating field
- Closure-characteristic subgroup
- Cocentral subgroup
- Cofactorial automorphism-invariant subgroup
- Collection of groups satisfying a property-conditional congruence condition
- Collection of groups satisfying a universal congruence condition
- Collection of groups satisfying a universal non-divisibility condition
- Commutator-closed subgroup property
- Commutator-in-center subgroup
- Commutator-in-centralizer subgroup
- Commutator-realizable group
- Complemented central factor
- Complemented isomorph-containing subgroup
- Complemented transitively normal subgroup
- Completely divisibility-closed subgroup
- Completion-equivalent subgroups
- Composition factor-permutable group
- Composition factor-unique group
- Composition operator
- Composition series-unique group
- Conjugacy-closed normal subgroup
- Conjugacy-determined subgroup
- Conjugate-commensurable subgroup
- Conjugate-dense subgroup
- Conjugate-join-closed subgroup property
- Conjugate-join-closed subnormal subgroup
- Conjugate-large subgroup
- Conjugation-invariantly permutably complemented subgroup
- Conjugation-invariantly relatively normal subgroup
- Constructibly critical subgroup
- Contracharacteristic subgroup
- Coprime automorphism-faithful characteristic subgroup
- Coprime automorphism-faithful subgroup
- Coprime automorphism-invariant subgroup
- Core-characteristic subgroup
- Cring
- CS-extensible automorphism
- CS-pushforwardable automorphism
- CSCFN-realizable group
- Cyclic normal subgroup of finite group

### D

- Diagonal subgroup of a direct power
- Diagram-extensible automorphism
- Direct factor of characteristic subgroup
- Direct factor over central subgroup
- Direct product of subgroups of factors in direct product decomposition into cyclic groups
- Direct product-closed subgroup property
- Direct-product-closed subgroup property
- Directed union-closed group property
- Divisibility-closed subgroup
- Divisible normal subgroup
- Double coset-ordering subgroup
- Double coset-separated subgroup
- DRC-subgroup

### E

- EEP-subgroup
- Elementarily characteristic subgroup
- Encoding of an IAPS of groups
- Endo-invariance property
- Endoclinism-invariant subgroup
- Endomorph-dominating subgroup
- Endomorphism kernel
- Eventually simple IAPS
- Existence-bound-word subgroup
- Existentially bound-word subgroup
- Extended class-preserving automorphism
- Extensibility operator
- Extensible endomorphism

### F

- FACPC-subgroup
- Finitarily hypernormalized subgroup
- Finite abelian-strongly potentially characteristic subgroup
- Finite direct power-closed characteristic subgroup
- Finite group that is not isoclinic to a group of smaller order
- Finite-automorph-join-closed subnormal subgroup
- Finite-conjugate-join-closed subnormal subgroup
- Finite-dominating subgroup
- Finite-extensible automorphism
- Finite-extensible endomorphism
- Finite-Frattini-realizable group
- Finite-intersection-closed subgroup property
- Finite-iteratively extensible automorphism
- Finite-p-potentially characteristic subgroup
- Finite-p-potentially fully invariant subgroup
- Finite-pi-potentially characteristic subgroup
- Finite-pi-potentially fully invariant subgroup
- Finite-pi-potentially verbal subgroup
- Finite-potentially fully invariant subgroup
- Finite-quotient-pullbackable automorphism
- Finite-relative-intersection-closed subgroup property
- Formula automorphism
- Frattini-embedded normal-realizable group
- Frattini-in-center group
- Free-quotient subgroup
- Frugal Lazard-divided Lie ring
- Fully invariant subgroup of group of prime power order
- Fully invariant-potentially fully invariant subgroup
- Function property
- Function restriction-expressible subgroup property
- Fusion system-relatively strongly closed subgroup
- Fusion system-relatively weakly closed subgroup

### G

- GL IAPS
- Global LCS-Lazard Lie group
- Global LUCS-Lazard Lie group
- Global LUCS-Lazard Lie ring
- Global UCS-Lazard Lie group
- Group action property
- Group admitting a partition into abelian subgroups
- Group admitting a partition into cyclic subgroups
- Group extension operator
- Group having a class-inverting automorphism
- Group having an abelian conjugate-dense subgroup
- Group having an abelian contranormal subgroup
- Group having no proper isoclinic subgroup
- Group having no proper nontrivial transitively normal subgroup
- Group in which any two characteristic subgroups are comparable
- Group in which every automorph-conjugate subgroup is characteristic
- Group in which every automorphism is normal-extensible
- Group in which every characteristic subgroup is powering-invariant
- Group in which every element is automorphic to its inverse
- Group in which every endomorphism is trivial or an automorphism
- Group in which every locally inner automorphism is inner
- Group in which every normal subgroup is powering-invariant
- Group in which every normal-extensible automorphism is inner