What would you like to understand?

A normal subgroup (also called an invariant subgroup) is a subgroup H of a group G such that all conjugates of every element in H belong to H. Algebraically, this condition is expressed as $gHg^{-1} = H$ for any element $g$ in G.

Conditions: H is a subgroup of G; The condition must hold for all elements in H; The condition must hold for all elements g in G

A normal subgroup (also called an invariant subgroup) is a subgroup H of a group G such that all conjugates of every element in H belong to H. Algebraically, this condition is expressed as $gHg^{-1} = H$ for any element $g$ in G.

Conditions: H is a subgroup of G; The condition must hold for all elements in H; The condition must hold for all elements g in G

In the context of group theory, $gH$ represents the left coset of the subgroup H with respect to the element g, while $Hg$ represents the right coset of H with respect to g. For a normal subgroup, these two sets are identical.

Conditions: H is a subgroup of G; g is an element of the group G

In the context of group theory, $gH$ represents the left coset of the subgroup H with respect to the element g, while $Hg$ represents the right coset of H with respect to g. For a normal subgroup, these two sets are identical.

Conditions: H is a subgroup of G; g is an element of the group G