I have been using Fraleigh's book, A first course in abstract algebra There is one thing I want you to ask whether the definition of solvable group in this book is right or not.
In my book, definition of Solvable group is as follows
A group $G$ is solvable if it has a composition series $\{H_i\}$ such that all factor groups $H_{i+1}/H_i$ are Abelian.
But most of other book give quite different definition of solvable group. They define it :
A group $G$ is solvable if it has a subnormal seires $\{H_i\}$ such that all factor groups $H_{i+1}/H_i$ are Abelian.
are these two definition equivalent?