# Normal coalition class

From Groupprops

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

View a complete list of group metaproperties

This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

## 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 of groups is said to give a **normal coalition class** if whenever is a group and and are normal subgroups of both satisfying as groups, then the subgroup also satisfies .

## Examples

- The group property of being finite