DRC-subgroup

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]

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Definition

Symbol-free definition

A subgroup of a group is said to be a DRC-subgroup if its characteristic closure is the direct product of itself with subgroups isomorphic to it, viz its characteristic closure is a direct power of it, or equivalently, if it is a direct root in its characteristic closure.

Relation with other properties

Stronger properties

• Direct root
• Characteristic subgroup
• Minimal normal subgroup: For full proof, refer: Minimal normal implies DRC

Weaker properties

• DFC-subgroup
• 2-subnormal subgroup