Right-quotient-transitively central factor
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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]
This is a variation of central factor|Find other variations of central factor |
Definition
Definition with symbols
A subgroup of a group
is termed a right-quotient-transitively central factor if
is a normal subgroup of
and whenever
is a subgroup of
such that
is a central factor of
, then
is a central factor of
.
Relation with other properties
Stronger properties
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