The book you are looking for is titled "Topics in Abstract Algebra" by M.K. Sen, Shamik Ghosh, and Parthasarathi Mukhopadhyay. It is a widely used textbook for undergraduate and postgraduate mathematics students in India, specifically designed to align with the UGC Choice Based Credit System (CBCS) syllabus. Key Features and Content

Who it’s best for: Undergraduates or beginning graduate students who want a concise, conventional treatment to learn techniques and prepare for exams; suitable as a course companion or reference.

Exercises: A healthy mix of routine and challenging problems. Good for practicing technique and for course use; however, problem sets occasionally lack hints or solutions.

New Additions: This edition introduces a section on the Automorphism of Groups and includes Multiple Choice Questions (MCQs) at the end of each section to aid competitive exam preparation.

Competitive Exam Prep: Exercises include Multiple Choice Questions (MCQs) designed for NET, JAM, GATE, and TIFR aspirants.

• Google Books: Often offers a preview of the text which is sufficient for checking specific chapters.
• University Libraries: Many university digital libraries subscribe to platforms that host this text.
• Publisher’s Website: Checking Universities Press (India) for an e-book edition supports the authors and ensures you get the latest corrected version.

In its treatment of Group Theory, the book is exhaustive. It covers the basic definitions, subgroups, cyclic groups, and permutation groups. A significant strength of the text is its treatment of Lagrange’s Theorem and the Sylow Theorems. These are often stumbling blocks for students, but the authors provide ample examples and proofs that are detailed rather than terse. The inclusion of solved examples is a critical feature; in mathematics, seeing a proof written out in full allows a student to mimic the logical structure in their own exercises.