  This paper provides the first steps in classifying the finite solvable groups
having Property A, which is a property involving abelian normal subgroups. We
see that this classification is reduced to classifying the solvable
Chermak-Delgado simple groups, which the author defines. The author completes a
classification of Chermak-Delgado simple groups under certain restrictions on
the primes involved in the group order.
