Subgroup containing the center
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Subgroups containing the center are important in the context of isoclinisms. They are also important in the sense of being "big enough" in some ways. For instance, in a nilpotent group, any subgroup containing the center is "big enough" to contain all the relevant torsion (see equivalence of definitions of nilpotent group that is torsion-free for a set of primes).