Finite simple groups Abstract finite groups Algebraic topology -- Applied homological algebra and category theory -- Applied homological algebra and category theory Algebraic topology -- Homotopy theory -- Homotopy theory Classifying spaces Combinatorics -- Algebraic combinatorics -- Group actions on combinatorial structures Connections with homological algebra and category theory Finite groups Finite simple groups and their classification Group theory Group theory and generalizations Group theory and generalizations -- Abstract finite groups -- Finite simple groups and their classification Group theory and generalizations -- Abstract finite groups -- Series and lattices of subgroups Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type Group theory and generalizations -- Abstract finite groups -- Simple groups: sporadic groups Group theory and generalizations -- Connections with homological algebra and category theory -- Homological methods in group theory Group theory and generalizations -- Representation theory of groups -- Representations of finite groups of Lie type Group theory and generalizations -- Representation theory of groups -- Representations of sporadic groups Linear algebraic groups and related topics Permutation groups Representation theory of groups Representations of groups Research exposition (monographs, survey articles) Sporadic groups (Mathematics) Structure and classification of infinite or finite groups