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closed as a duplicate of: Group theory doubt
asked in Set Theory & Algebra by Active (1k points)
closed by | 71 views

In cycle group if a is generator then it will generate all elements. i.e. a10= e

If a generator then (a8)x = (a10) = e

put x= 1,2,3,4,5,6,7,8,.... take smallest x which satisfy this 

(a8)5 = (a10) = e

(a10)4 = (a10) = e

8 also satisfy but order will be smallest such value satisfy the conditionl. hence 5 is answer

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