What does normal subgroup mean?
Definitions for normal subgroup
nor·mal sub·group
This dictionary definitions page includes all the possible meanings, example usage and translations of the word normal subgroup.
Wiktionary
normal subgroupnoun
A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg is in H.
Wikipedia
Normal 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 {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and only if g n g − 1 ∈ N {\displaystyle gng^{-1}\in N} for all g ∈ G {\displaystyle g\in G} and n ∈ N . {\displaystyle n\in N.} The usual notation for this relation is N ◃ G . {\displaystyle N\triangleleft G.} Normal subgroups are important because they (and only they) can be used to construct quotient groups of the given group. Furthermore, the normal subgroups of G {\displaystyle G} are precisely the kernels of group homomorphisms with domain G , {\displaystyle G,} which means that they can be used to internally classify those homomorphisms. Évariste Galois was the first to realize the importance of the existence of normal subgroups.
Wikidata
Normal subgroup
In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup H of a group G is normal in G if and only if gH = Hg for all g in G. Normal subgroups can be used to construct quotient groups from a given group. Évariste Galois was the first to realize the importance of the existence of normal subgroups.
Numerology
Chaldean Numerology
The numerical value of normal subgroup in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of normal subgroup in Pythagorean Numerology is: 3
Translations for normal subgroup
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"normal subgroup." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/normal+subgroup>.
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