Normal equals strongly image-potentially characteristic
From Groupprops
This article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup
View a complete list of pages giving proofs of equivalence of definitions
Contents
Statement
The following are equivalent for a subgroup of a group
:
-
is a normal subgroup of
.
-
is a strongly image-potentially characteristic subgroup of
in the following sense: there exists a group
and a surjective homomorphism
such that both the kernel of
and
are characteristic subgroups of
.
Related facts
- NPC theorem
- NRPC theorem
- Finite NPC theorem
- Finite NIPC theorem
- Fact about amalgam-characteristic subgroups: finite normal implies amalgam-characteristic, periodic normal implies amalgam-characteristic, central implies amalgam-characteristic