# Core-free 2-subnormal subgroup

From Groupprops

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: core-free subgroup and 2-subnormal subgroup

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## Definition

A subgroup of a group is termed a **core-free 2-subnormal subgroup** if it is both a core-free subgroup (i.e., its normal core is trivial) and a subnormal subgroup.