Normal Subgroup

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If

 xHx^(-1)=H

for every element x in G, then H is said to be a normal subgroup of G, written H<|G . Normal subgroups are also known as invariant subgroups or self-conjugate subgroup.

All subgroups of Abelian groups are normal

Author: Deepak Chahar

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