(1) Let G be a group such that
Show that G cannot be cyclic.
(2) Show that a cyclic group with one generator has at most 2 elements.
(3) Let a 2 G be an element of order two, and b 2 G an element of order three. Show that HK where H = (a) and K = (b) has order 6.
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Cyclic groups, generators and orders of elements are investigated. The solution is detailed and well presented.