A maximal normal subgroup is a subgroup of a group that is normal (invariant under conjugation) and is not properly contained in any other normal subgroup. In other words, it is the largest possible normal subgroup within a given group.
A maximal normal subgroup is unique in that it cannot be properly contained in any other normal subgroup. This means that it is the biggest normal subgroup within a group.
Maximal normal subgroups play an important role in the structure and classification of groups. They can be used to determine the structure of a group and its subgroups, and are essential in understanding the properties of a group.
Identifying a maximal normal subgroup requires knowledge of the group's structure and its normal subgroups. It can also involve using specific algorithms or techniques to determine the largest normal subgroup within a group.
Yes, a group can have multiple maximal normal subgroups. However, these subgroups will be distinct and not properly contained within each other. In other words, they will be separate and non-overlapping.