In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group...

form a subgroup of index 2 in S, called the alternating subgroup A. Since A is even a characteristic subgroup of S, it is also a normal subgroup of the...

important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian. In other words, G / N...

{\displaystyle gHg^{-1}} of a subgroup H in G is equal to the index of the normalizer of H in G. If H is a subgroup of G, the index of the normal core of H satisfies...

characteristic subgroup is normal; though the converse is not guaranteed. Examples of characteristic subgroups include the commutator subgroup and the center...

element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting...

{\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...

special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p-core of a group. For a group G, the normal core...

group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it...