With which monoid is (Z/24Z,+,0) isomorphic?
(Z/8Z,+,0) × (Z/3Z,+,0)
(Z/12Z,+,0) × (Z/12Z,+,0)
(Z/12Z,+,0) × (Z/2Z,+,0)
Yes, by the Chinese Remainder Theorem.
No, the order(=number of elements) of this monoid equals 144, which differs from the order of
Z/24Z.
No, the sizes fit, but the structures are different.
For instance, there is no element g in this monoid such that
the whole monoid is {e, g, g2, ...},
whereas there is such an element in Z/24Z.