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GeezerVison is showing mathworld.wolfram.com — Conjugate Subgroup -- from Wolfram MathWorld

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Conjugate Subgroup

A conjugate subgroup of a subgroup H of a group G is the subgroup xHx^(-1)={xhx^(-1):h in H}, where x is any group element of G. If xHx^(-1)=H for all x in G, then H is a normal subgroup (also called "self-conjugate" or "invariant").

All subgroups of an Abelian group are normal subgroups.

See also

Normal Subgroup, Subgroup, Sylow Theorems

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  • Abelian group
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Cite this as:

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

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