third isomorphism theorem

If $G$ is a group (or ring, or module) and $H$ and $K$ are normal subgroups (or ideals, or submodules, respectively) of $G$, with $H\subseteq K$, then there is a natural isomorphism $(G/H)/(K/H)\cong G/K$.

This is usually known either as the Third Isomorphism Theorem, or as the Second Isomorphism Theorem (depending on the order in which the theorems are introduced). It is also occasionally called the Freshman Theorem.

Title	third isomorphism theorem
Canonical name	ThirdIsomorphismTheorem
Date of creation	2013-03-22 12:04:03
Last modified on	2013-03-22 12:04:03
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	12
Author	yark (2760)
Entry type	Theorem
Classification	msc 20A05
Classification	msc 13A15
Classification	msc 16D10
Synonym	freshman theorem