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Using the Mathematics Subject Classification system
Searching by Mathematical Subject Classification (MSC):
Zoom in on very specialized literature.
Or zoom out to find general expositions.
Example: Find a graduate-level exposition of group theory, offering many exercises on the Sylow Theorems.
Go to the MSC page to find the MSC 20-01: "Group theory and generalizations: Instructional exposition (textbooks, tutorial papers, etc.)"
Input " 20-01" in MathSciNet under "MSC Primary."
Input " Sylow and exercises" in MathSciNet under "Anywhere."
Under "Publication Type," choose " Books" (to get graduate level expositions).
Open and scan results. As of August 2020, there were 16 results.
Look at Adam Glesser's review of Antonio Machi's book, Groups: An introduction to ideas and methods of the theory of groups. Glessner's review emphasizes the "copious exercises" and that "nearly every section has several well-chosen illustrations of the theory." Glesser mentions "Sylow theorems" (which was a search keyword).
Search in Springerlink database to find the book (link at book title in previous step).
Find chapter 3 on "Group Actions and Permutation Groups. Section 3.2 on "Sylow Theorems" does indeed have many illustrations of the theory and many exercises.