Nilpotent groups are a class of groups where the upper central series terminates in the group itself. This means that every normal subgroup of the group has a non-trivial intersection with the center of the group. These groups are important because they exhibit certain properties that connect to solvable groups, as all nilpotent groups are also solvable, but not all solvable groups are nilpotent. They play a significant role in understanding the structure and classification of groups.
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