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Property:Quick phrase

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Pages using the property "Quick phrase"

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C
Central factor +factor in central product  +, product with centralizer is whole group  +, quotient action by outer automorphisms is trivial  +,
Characteristic closure +smallest characteristic subgroup containing  +, intersection of all characteristic subgroups containing  +, join of all automorphic subgroups  +
Characteristic subgroup +invariant under all automorphisms  +, automorphism-invariant  +, strongly normal  +,
Closure-characteristic subgroup +normal closure is characteristic  +, join of all conjugates is characteristic  +
Core-characteristic subgroup +intersection of all conjugates is characteristic  +, normal core is characteristic  +
Cosimplicial group +cosimplicial object in category of groups  +, group object in category of cosimplicial sets  +
Countable group +countable  +, countably generated  +
D
Dedekind group +every subgroup is normal  +, every cyclic subgroup is normal  +, normal closure of element is cyclic  +
Direct factor +factor in internal direct product  +, normal with normal complement  +, has centralizing complement  +
F
Fully invariant subgroup +invariant under all endomorphisms  +, endomorphism-invariant  +
G
Group of nilpotency class two +class two  +, inner automorphism group is abelian  +, commutator subgroup inside center  +,
Group whose automorphism group is abelian +abelian automorphism group  +, any two automorphisms commute  +
Gyrogroup +left identity, left inverses and associativity twisted by an automorphism  +
H
H-group +topological space with continuous operations that satisfy homotopy versions of group laws  +
Hypergroup +variation of group where the multiplication operation is multi-valued  +
I
Injective endomorphism-invariant subgroup +invariant under all injective endomorphisms  +, injective endomorphism-invariant  +
Inverse semigroup +semigroup where every element has a unique ''inverse'' in the semigroup sense (i.e., without reference to neutral elements)  +
Isomorph-containing subgroup +contains all isomorphic subgroups  +, weakly closed in any ambient group  +
Isomorph-free subgroup +no other isomorphic subgroups  +, no isomorphic copies  +, only subgroup of its isomorphism type  +
L
Lie ring of nilpotency class two +class two  +, inner derivation Lie ring is abelian  +, derived subring inside center  +,
Loop +group without associativity  +, unital magma with unique left and right quotients  +
M
Metabelian group +abelian-by-abelian  +, abelian normal subgroup with abelian quotient  +, abelian derived subgroup  +,
Monoid +group without inverses  +, set with associative binary operation with identity element  +, semigroup with identity element (neutral element)  +
Moufang loop +loop (identity, inverses, not necessarily associative) with some associativity-like conditions that come close to making it a group  +
Multiary group +group-like structure with n-ary instead of binary operation for multiplication  +