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Third Group Isomorphism Theorem

Let G be a group having normal subgroups H and K with H subset= K. Then K/H⊴G/H and

(G/H)/(K/H)=G/K,

where N⊴G indicates that N is a normal subgroup of G and G=H indicates that G and H are isomorphic groups.

See also

First Group Isomorphism Theorem, Fourth Group Isomorphism Theorem, Second Group Isomorphism Theorem

This entry contributed by Nick Hutzler

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References

Dummit, D. S. and Foote, R. M. "The Isomorphism Theorems." §3.3 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 97-100, 2004.

Referenced on Wolfram|Alpha

Third Group Isomorphism Theorem

Cite this as:

Weisstein, Eric W., with contributions by Nick Hutzler. "Third Group Isomorphism Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThirdGroupIsomorphismTheorem.html

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