Normal coalition class

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This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
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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 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_1H_2 also satisfies p.

Examples