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1 (i) Let Cn = {e, x, ..., xn-1} (xn = e) be the cyclic group of order n and let H be a subgroup of Cn . By considering min{i > 0 : xi ∈ H} show that H = (xm) for some m|n.
(ii) Find all subgroups of C18, explaining your answer.
2(i) Find (a) 41602 (mod 17), (b) 4-1 (mod 17), (c) 41597 (mod 17)
(ii) Find (a) 11-1 (mod 13), (b) 111198 (mod 13)
Attachment:- Maths-Groups.pdf
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