Find the number of elements in the indicated cyclic group. The cyclic subgroup of z225 generated by 45.

Part 1 Find the number of elements in the cyclic group of generated by 6. Let a*b = ab - 2 show if it is commutative, associative binary operation on Z ? give the identity element and inverse element   Part 2 picture is for part 2 only  1.Compute a * b 2.Compute [(a * b) * c] * d 3.Compute [a (b * c)] * b

The following is a Cayley table for a group G. 2*5 4 = 3 5| 2 3 4 3 4 1 4 5 2 1 2 3. 4 2 4 234 5 23 45

find the order of the cyclic group of the given group generated by the indicated element. The subgroup of the symmetric group S8 generated by (2,4,6,9)(3,5,7)