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Second Group Isomorphism Theorem


The second, or diamond, group isomorphism theorem, states that if G is a group with A,B subset= G, and A subset= N_G(B), then (A intersection B)⊴A and AB/B=A/A intersection B, where N⊴G indicates that N is a normal subgroup of G and G=H indicates that G and H are isomorphic groups.

This theorem is so named because of the diamond shaped lattice of subgroups of G involved.


See also

First Group Isomorphism Theorem, Third Group Isomorphism Theorem, Fourth Group Isomorphism Theorem

This entry contributed by Nick Hutzler

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References

Dummit, D. S. and Foote, R. M. Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 98-100, 1998.

Referenced on Wolfram|Alpha

Second Group Isomorphism Theorem

Cite this as:

Hutzler, Nick. "Second Group Isomorphism Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SecondGroupIsomorphismTheorem.html

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