Normal subgroup

In abstract algebra, a normal 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 ∈ N for all g ∈ G and n ∈ 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 are precisely the kernels of group homomorphisms with domain 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.

Words

This table shows the example usage of word lists for keywords extraction from the text above.

WordWord FrequencyNumber of ArticlesRelevance
normal7159320.304
subgroup521340.291
g8437580.287
subgroups47560.264
n61012990.178

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