if we've given any order of group then how can we check that is it cyclic or not example how can we check group of order 255 and 465 and 3000 order cyclic or not.Please help
If with primes and then . Otherwise then it is not true.
Now there the group is not necessarily cyclic.
Note let be a non-cyclic group of order . Then and is not cyclic.
If where then we can construct a non-abelian group - the dihedral.
Therefore a group of order is not necessarily cyclic.