Math and science::Algebra::Aluffi

Normal subgroup

Let $G$ be a group and $N$ a subgroup of $G$ .

$N$ is said to be normal iff:

[

\forall n \in N, \forall g \in G, ?

]

Or equivalently:

[

N is normal ⟺ \forall g \in G, ?

]

$g N$ is syntax for ${a : a = g n for some n \in N}$ , and $g N = N g$ does not imply commutativity.

04.04.2022