A normal subgroup of a group is a subgroup satisfying

for every element . This condition is written (Arfken 1985, p. 242; Scott 1987, p. 25). Normal subgroups are also called invariant subgroups or self-conjugate subgroups (Arfken 1985, p. 242).

All subgroups of Abelian groups are normal (Arfken 1985, p. 242).

See also

Abelian Group, Group, Margulis-Platonov Conjecture, Normal Closure, Normal Factor, Normal Series, Quotient Group, Subgroup Explore this topic in the MathWorld classroom

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.Scott, W. R. Group Theory. New York: Dover, 1987.

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Normal Subgroup

Cite this as:

Weisstein, Eric W. "Normal Subgroup." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NormalSubgroup.html

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