Question

Consider the group S3. (i) Show that S3 has precisely six subgroups, of which precisely three...

Consider the group S3.

(i) Show that S3 has precisely six subgroups, of which precisely three are normal.

(ii) Describe the equivalence relation associated to each subgroup, as well as the left cosets and the right cosets.

(iii) Describe the group structure of all quotients of S3 modulo one of the three normal subgroups.

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