Let and . is cyclic of order 8.

Show that is cyclic.

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- Sep 9th 2011, 12:26 PMskykingProve quotient group cyclic
Let and . is cyclic of order 8.

Show that is cyclic. - Sep 10th 2011, 03:17 AMModusPonensRe: Prove quotient group cyclic
I'm not sure my solution is correct, but here it goes.

I assume is a cyclic group of order 8. So H is isomorphic , or to . So is isomorphic to , which is isomorphic to , which is isomorphic to , which is a cyclic group.

Edited to, hopefuly, correct the mistakes. - Sep 10th 2011, 06:54 AMskykingRe: Prove quotient group cyclic
Thanks, You are correct. We have atheorem that states .