Normal coalition class

This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
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History

Origin of the term

The term normal coalition class was introduced by J.E. Roseblade in the paper On Certain Subnormal Coalition Classes in Journal of Algebra, I, 132-138 (1964).

Definition

Definition with symbols

A group property $p$ of groups is said to give a normal coalition class if whenever $G$ is a group and $H_1$ and $H_2$ are normal subgroups of $G$ both satisfying $p$ as groups, then the subgroup $H_1{H}_2$ also satisfies $p$.

Examples

• The group property of being finite