third isomorphism theorem

If G is a group (or ring, or module) and H and K are normal subgroupsMathworldPlanetmath (or ideals, or submodulesMathworldPlanetmath, respectively) of G, with HK, then there is a natural isomorphism (G/H)/(K/H)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