Question 9
A ring $(A, +, \cdot)$ has property (P) if $A$ is finite and the multiplicative group of units is isomorphic to a non-trivial subgroup of the additive group $(A, +)$. Show that:
(a) the number of elements of a ring having property (P) is even;
(b) there are $n$-element rings having property (P) for infinitely many positive integers $n$.
(a) the number of elements of a ring having property (P) is even;
(b) there are $n$-element rings having property (P) for infinitely many positive integers $n$.