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Find all the subgroups of a cyclic group of order 12.

(A) {e},(a6),(a4),(a3),(a2),(a)

(B) (a12),(a6),(a4),(a3),(a2),(a)

(C) (a12),(a6),(a4),(a2),(a)

(D) (a12),(a6),(a4),(a3),(a2),(a),{e}

asked in Set Theory & Algebra by Boss (11.4k points) | 309 views

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for all group G ....'G' and e are trivial subgroups and now by using lagrenges theorm...

ORDER OF SUBGROUP MUST DIVIDE THE ORDER OF GROUP....

so correct answer will we

D) as all subgoups's degree divide the MAIN GROUPS ORDER....
answered by Boss (10.8k points)
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order of a subgroup must divide the order of group but it does not necessarily mean all that divisors are a subgroup 

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