Upper central series-comparable group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A nilpotent group is termed upper central series-comparable if it satisfies the following equivalent conditions:

  1. Every member of its upper central series is comparable with all normal subgroups
  2. Every normal subgroup of the group is between two adjacent members of its upper central series

Relation with other properties

Stronger properties