Right-quotient-transitively central factor

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Right-quotient-transitively central factor, all facts related to Right-quotient-transitively central factor) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

This is a variation of central factor|Find other variations of central factor |

Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a right-quotient-transitively central factor if $H$ is a normal subgroup of $G$ and whenever $K$ is a subgroup of $G$ such that $K/H$ is a central factor of $G/H$, then $K$ is a central factor of $G$.

Relation with other properties

Stronger properties

• Direct factor
• Cocentral subgroup

Weaker properties

• Join-transitively central factor: For proof of the implication, refer Right-quotient-transitively central factor implies join-transitively central factor and for proof of its strictness (i.e. the reverse implication being false) refer Join-transitively central factor not implies right-quotient-transitively central factor.
• Central factor
• Transitively normal subgroup
• Normal subgroup