ATLAS of Finite Groups

The ATLAS of Finite Groups, published by Oxford University Press in 1985, serves as a comprehensive reference text documenting the properties of 93 finite simple groups. The work represents a collaboration between mathematicians John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker, and Robert Arnott Wilson. The book presents detailed information about each group, including orders, Schur multipliers, outer automorphism groups, and character tables. Its distinctive spiral-bound format and systematic organization make it a practical tool for mathematicians working with group theory. The ATLAS covers all 26 sporadic groups and selected examples from infinite families of groups, with the authors choosing to include groups that extend slightly beyond what they considered reasonable coverage. The work includes previously unpublished discoveries from Conway's Cambridge University research group. The ATLAS stands as a foundational text in group theory, representing a pivotal moment in the systematization and documentation of mathematical knowledge about finite groups. Its influence continues to shape research and understanding in abstract algebra.

Readers describe this as a dense mathematical reference book used primarily by group theory specialists and researchers. Most reviews come from academic sources rather than general review sites. Likes: - Comprehensive tables and data on finite simple groups - Detailed character tables - Clear organization and layout - Valuable resource for checking calculations Dislikes: - Very expensive ($400+ for hardcover) - Physical size makes it unwieldy - Some reported printing errors in early editions - Too specialized for non-experts One mathematician noted: "It sits on my shelf like a phone book, but contains invaluable data I reference frequently in research." Review Sources: Goodreads: No ratings Amazon: 5/5 (1 review) Mathematical Reviews: Multiple detailed academic reviews praising its technical merit but noting high cost zbMATH: Referenced in 250+ citations as an authoritative source The specialist nature means few public reviews exist outside academic journals and conference proceedings.

Character Theory of Finite Groups by I. Martin Isaacs Contains detailed character tables and theoretical foundations that complement the ATLAS's computational focus on finite simple groups.

Groups and Characters by Larry Dornhoff Provides theoretical background and computational methods for constructing character tables that users of the ATLAS utilize in practice.

The Theory of Group Representations by Francis D. Murnaghan Presents representation theory tools that explain the underlying structure behind the data compiled in the ATLAS.

Simple Groups of Lie Type by Roger Carter Examines the classification of finite groups of Lie type, covering many of the families documented in the ATLAS.

Finite Simple Groups: An Introduction to Their Classification by Daniel Gorenstein Explains the theory behind the classification of finite simple groups that forms the organizational basis of the ATLAS.

🔢 The book's distinctive cherry-red color was chosen deliberately to make it instantly recognizable on mathematicians' shelves 📊 It took over 15 years to complete the ATLAS, involving complex computations that pushed the limits of 1980s computer technology 🎲 John Conway, the lead author, is also famous for creating "Conway's Game of Life" - a mathematical simulation that helped pioneer cellular automata 📚 The work's standardized format for presenting group information has become so influential that it's known as "ATLAS notation" in mathematical literature 🏆 The documentation of all 26 sporadic groups in one place was unprecedented at the time, making the ATLAS a breakthrough in understanding these exceptional mathematical structures