Build up the operation tables for group G with orders 1, 2, 3 and 4 using the elements a, b, c, and e as the identity element in an appropriate way. 2. i. State the Lagrange’s theorem of group theory. ii. For a subgroup H of a group G, prove the Lagrange’s theorem. iii. Discuss whether a group H with order 6 can be a subgroup of a group with order 13 or not. Clearly state the reasons.
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