# Cosets of Subgroups of a Group

Modern Algebra

Group Theory (XXVII)

Subgroups of a Group

Cosets of Subgroups of a Group

For a subgroup H of G define a left coset of H in G as the set of all elements of the form ah, h in H.

Show that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

The fully formatted problem is in the attached file.

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#### Solution Summary

It shows that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

The solution is detailed and well presented.

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