24.
25.
26.

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Section C

Answer any two questions.
Each question carries 10 marks.
Maximum 20 marks.

Show that the inverse of a group isomorphism is a group isomorphism.
Show that every sub-group of a cyclic group is cyclic.
Let H be a sub-group of the finite group G. Show that the order of H is a divisor of order of G.

State and prove First Isomorphism Theorem.

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