Ascending chain condition on subnormal subgroups is normal subgroup-closed

This article gives the statement, and possibly proof, of a group property (i.e., group satisfying ascending chain condition on subnormal subgroups) satisfying a group metaproperty (i.e., normal subgroup-closed group property)
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Statement

Property-theoretic statement

The property of being a group satisfying ascending chain condition on subnormal subgroups is a normal subgroup-closed group property.

Statement with symbols

Suppose $G$ is a group satisfying ascending chain condition on subnormal subgroups and $N$ is a normal subgroup of $G$. Then, $N$ is also a group satisfying ascending chain condition on subnormal subgroups.

Related facts

Applications

• Ascending chain condition on subnormal subgroups implies subnormal join property