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Was (wer) ist hyperelementary subgroup - definition
Subgroup diagram; Subgroup lattice
![cycle graphs]]](https://commons.wikimedia.org/wiki/Special:FilePath/Dih4 subgroups (cycle graphs).svg?width=200 "cycle graphs]]")
Normal subgroup
SUBGROUP INVARIANT UNDER CONJUGATION
Normal subgroups; Invariant subgroup; ◅; Normal group; ⊲; ⊳; ⊴; ⊵; ⋪; ⋫; ⋬; ⋭; Normal Subgroup; Self-conjugate subgroup
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N of the group G is normal in G if and only if gng^{-1} \in N for all g \in G and n \in N.
Commutator subgroup
SMALLEST NORMAL SUBGROUP BY WHICH THE QUOTIENT IS COMMUTATIVE
Derived subgroup; Abelianisation; Abelianization; Derived group; Derived series; Transfinite derived series; The Commutator Subgroup Of G; The Derived Group Of G; Commutator group
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
Subgroup
![60px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Alternating group 4; Cayley table; numbers.svg?width=200 "60px]]")
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; subgroup of S4.svg?width=200 "70px")
; subgroup of S4.svg?width=200 "70px")
; subgroup of S4.svg?width=200 "70px")
![70px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Dihedral group of order 8; Cayley table (element orders 1,2,2,2,2,4,4,2); subgroup of S4.svg?width=200 "70px]]")
![70px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Dihedral group of order 8; Cayley table (element orders 1,2,2,4,2,2,4,2); subgroup of S4.svg?width=200 "70px]]")
![70px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Dihedral group of order 8; Cayley table (element orders 1,2,2,4,4,2,2,2); subgroup of S4.svg?width=200 "70px]]")
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![additive group]]). Together they partition the entire group G into equal-size, non-overlapping sets. The index [G : H] is 4.](https://commons.wikimedia.org/wiki/Special:FilePath/Left cosets of Z 2 in Z 8.svg?width=200 "additive group]]). Together they partition the entire group G into equal-size, non-overlapping sets. The index [G : H] is 4.")
![60px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 3; Cayley table; subgroup of S4 (elements 0,1,14,15,20,21).svg?width=200 "60px]]")
![60px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 3; Cayley table; subgroup of S4 (elements 0,1,2,3,4,5).svg?width=200 "60px]]")
![60px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 3; Cayley table; subgroup of S4 (elements 0,2,6,8,12,14).svg?width=200 "60px]]")
![60px]]](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 3; Cayley table; subgroup of S4 (elements 0,5,6,11,19,21).svg?width=200 "60px]]")
![The [[symmetric group]] S<sub>4</sub> showing all [[permutation]]s of 4 elements](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 4; Cayley table; numbers.svg?width=200 "The [[symmetric group]] S<sub>4</sub> showing all [[permutation]]s of 4 elements")
SUBSET OF A MATHEMATICAL GROUP THAT FORMS A GROUP ITSELF
SubGroup; Subgroups; Proper subgroup; Overgroup; Subgroup test; Subgroup Test; Sub-group; Subgroup (mathematics); Subgroups of S4
·noun A subdivision of a group, as of animals.
Wikipedia
Lattice of subgroups
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In mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial order relation being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection.
