Image-potentially fully invariant subgroup
From Groupprops
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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]
Definition
Suppose is a subgroup of a group
. We say that
is an image-potentially fully invariant subgroup of
if there exists a group
, a surjective homomorphism
, and a subgroup
of
such that
.
Relation with other properties
Stronger properties
property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|
Fully invariant subgroup |
Weaker properties
property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
---|---|---|---|---|
Normal subgroup |