Group theory problems manual It would be really a worthy contribution if someone please,From the point of view ,of covering all the problems which are based on application of theorems of group theory, recommend a manual of problems with solutions. 
The book which satisfies following conditions:


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*It should contain large set of problems on group theory with solution

*Problems should NOT be Proofs.., Show That.. types but instead They SHOULD be based on their applications.example : number of generators of of cyclic group having the given order... or number of homomorphisms between given groups etc... 
In short it should not focus on problems involving proofs,But their applications.

*Book like Abstract algebra Problem and solution by ayman badawi. Which unfortunately is probably not available in SAARC countries.
Is it possible to list such books along with links?
 A: Below I will list some Group Theory books which contain at least partial solutions. 
Regarding your point that you wish for the problems to be based on applications of results rather than proving results, I think this severely restricts the texts available. I am sure almost all the texts I am about to list will contain problems of both styles, and I think if a reader wishes to find problems of just one style and have solutions their best bet is to look over the texts below and just do the questions you like the look of.
Schaums Outline of theory and problems in Group Theory - I think this is an excellent text and is the first text I would recommend to a friend who wanted to begin solving problems in group theory. I know that Schaums guides have a mixed reputation, but the Group Theory text is excellent. It is just like a regular textbook, except it includes many examples and problems with solutions. Some of the problems are hard proofs, but many are computational, straight forward or involve applying a theorem or understanding a definition. 
The book - “A course in group theory” by John F Humphreys is an excellent introduction to group theory, and in fact it goes quite far. It has many worked examples, and there are solutions to the exercises at the back. 
Another group theory problem book with solutions is “Problems in group theory” by J. D Dixon. The problems in this book are in my opinion quite hard compared to the previous books, and many of the problems are of the style which you do not want - they involve you proving results for yourself. However it also contains some more computational questions. I would definitely recommend you take a look at this book if you have access to it, but I don’t think it is the ideal book you are after. 
I also mention here that the book “Representations and Characters of groups”, contains solutions at the end of the book for the exercises. The book is very accessible and many of the exercises are of the style you want. However as the title suggests, the focus here is on Representation and Character theory of groups. 
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The books listed above are ones I have studied from extensively myself. However I also think that the book Contemporary Abstract Algebra by J. Gallian has solutions to some of the exercises, and furthermore I think that you might be able to find answers to the other questions on the internet. 
On this note, one suggestion I have for you is to look for group theory problem sheets and solutions from other universities. For example if you search for “homework solutions finite abelian group” the first result I get is a problem sheet with solutions involving applications of the structure theorem of finite abelian groups.
