can somebody recommend a book in a group theory. can somebody recommend a book in a group theory. that include just questions and their answers. $without$ $theory!$

Actually, there is such a book. Yaglom's Geometric Tansformations is a classic text which basically makes you answer lots of questions as opposed to simply presenting the theory to you. The answers are at the back of the English version.
However, this text is not a classic group theory book. It is about one facet of group theory - isometries - rather than the theory as a whole.
Interesting point: it was translated into English from the original Russian as part of the "New Math" course in the United States, which was meant as a way of getting the maths level of the USA in line with that of Russia. So this is a school book. However, the Russians said that they would never, ever, under any circumstances, base a school course on this book. The problems in this book are not exactly easy...
