Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.

Normal Subgroup

A subgroup that is invariant under conjugation by members of the group. Normal subgroups are crucial for constructing quotient groups.

📜

The statement of the theorem

A subgroup

N

G

is normal (denoted

N \trianglelefteq G

) if

gng^{-1} \in N

for all

n \in N

and

g \in G