Join of finitely many direct factors

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup of a group is termed a join of finitely many direct factors if it can be expressed as the join of finitely many subgroups, each of which is a direct factor of the whole group.

Relation with other properties

Stronger properties

• Direct factor: The strictness follows from the fact that direct factor is not finite-join-closed.

Weaker properties

• Join-transitively central factor
• Central factor
• SCAB-subgroup
• Conjugacy-closed normal subgroup
• Transitively normal subgroup
• Normal subgroup