Author Description

The Mathieu Groups Have Many Fascinating And Unusual Characteristics And Have Been Studied At Length Since Their Discovery. This Book Provides A Unique, Geometric Perspective On These Groups. The Amalgam Method Is Explained And Used To Construct M24, Enabling Readers To Learn The Method Through Its Application To A Familiar Example. The Same Method Is Then Used To Construct, Among Others, The Octad Graph, The Witt Design And The Golay Code. This Book Also Provides A Systematic Account Of 'small Groups', And Serves As A Useful Reference For The Mathieu Groups. The Material Is Presented In Such A Way That It Guides The Reader Smoothly And Intuitively Through The Process, Leading To A Deeper Understanding Of The Topic. The Mathieu Group M24 As We Knew It -- The Amalgam Method -- L4(2) In Two Incarnations And L3(4) -- From L5(2) To The Mathieu Amalgam -- M24 As Universal Completion -- Maximal Subgroups -- The 45-representation Of M24 -- The Held Group -- The Inevitability Of Mathieu Groups -- Locally Projective Graphs And Amalgams. A. A. Ivanov. Includes Bibliographical References And Index. 1. The Mathieu Group M₂₄ As We Knew It -- 1.1. The Golay Code -- 1.2. The Octad Graph -- 1.3. A Review -- 2. The Amalgam Method -- 2.1. Amalgams -- 2.2. Goldschmidt's Amalgams -- 2.3. Constrained Amalgams -- 2.4. Understanding Completions -- 2.5. The Mathieu Amalgam -- 3. L4(2) In Two Incarnations And L3(4) -- 3.1. The Fano Plane -- 3.2. The Group L3 (2) -- 3.3. Elements And Subgroups Of Li{2) -- 3.4. An Automorphism Of 23: L3(2) -- 3.5. Another Look At The Isomorphism L3(2) = L2(7) -- 3.6. A-7 And A Space Of Fano Planes -- 3.7. L4(2) = A8 -- 3.8. Subgroup Correspondence -- 3.9. Symplectic Identification -- 3.10. Restricting Automorphisms Of 23: L3(2) -- 3.11. Projective Plane Of Order 4 -- 3.12. Outer Automorphism Of S6 -- 4. From L5(2) To The Mathieu Amalgam -- 4.1. Maximal Parabolics In Gln (2) -- 4.2. Five-dimensional Gf(2)-space -- 4.3. The Universal Completion Of The Ls(2)-ama