Normal coalition class

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