Suppose that |G| = 24 and that G is cyclic. If a8 e and a12 e, show that = G.

UkusakazaL 2020-12-25 Answered

Suppose that |G|=24 and that G is cyclic. If a8 e and a12 e, show that = G.

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Expert Answer

delilnaT
Answered 2020-12-26 Author has 94 answers

Given that G is a cyclic group of order 24 and a,bG has order 8 and 12, respectively.

Now to show G=ab.

Since, G is cyclic, so it is abelian, So aa commutes with b. Therefore, order of ab=lcm(order of a, order of b)= lcm(8,12)=24.

Therefore, G=ab.

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