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The centre of a group is a normal subgroup of the group.

Modern Algebra
Group Theory (XXX)
Subgroups of a Group
Centre of a Group

If G is a group, the centre of G, Z is defined by Z = {z in G|zx = xz, all x in G}
Prove that Z is a subgroup of G.
Or,
Prove that Z is a normal subgroup of G .

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Solution Summary

This solution is comprised of a detailed explanation to prove that the centre of a group is a subgroup of the group.
It also explains that the centre of a group is also a normal subgroup of the group. The solution is detailed and well presented.

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