Question

Prove that any group of order 3 is cyclic.in hindi​

Answer 1

Answer:

it cannot be anything else

Step-by-step explanation:

if ab=a then b=e a contadiction if ab=b then a=e, a contradiction a2=because it cannot be anything else

Answer 2

Step-by-step explanation:

Let H be a group of order 3. By definition of group, there can be only one identity element in the group H.

So, H={e,x,y}.

By definition of cyclic group,

we have that the elements x and y

x=gn∃n∈Z

y=gn∃n∈Z

In particular, n is positive for if it were not, a contradiction would arise from having more than one identity element.

Any hints or assistance is appreciated.

Thank in advance.