Mathematics Homework Solutions
#129051
Prove that a subgroup is expressible as the union of conjugacy classes if and only if it is a normal subgroup.
Let G be a group, and let H be a subgroup of G. Prove that H is a normal subgroup if and only if H can be expressed as the union of conjugacy classes of G.
A detailed proof of the given assertion (that a subgroup H of a given group G is a normal subgroup if and only if H can be expressed as the union of conjugacy classes of G) is presented. The definitions of normal subgroup and conjugacy class are reviewed.
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