Cards看板

吹b用

• something
• Supersolvable Group
• Profinite Group
• Subgroup Lattice Theory by Gemini
• the Schreier-Sims Algorithm

Doing

• Symplectic group
• G2
• 好久之前的：
• Švarc-Milnor Lemma
• A5 is (5, 2, 3) & A4 is (3, 3, 2)
• Affine Group
• Suzuki p-group
• Goursat’s Lemma
• a Lemma of Cohomology
• Classification of Quasiprimitive Rank 3 Groups
• Automorphism Groups of Direct Product of Isomorphic Simple Groups
• Minimal Normal Subgroups of Permutation Groups
• Three Permutations on G Induced from G
• Singer Cycle
• Examples of (Quasi)primitive
• Characteristic Subgroup
• Group Core
• Characteristically Simple

Todo

• Exterior Algebra
• Schur Multiplier
• Cohomology lemmas
• Lüroth’s theorem
• Normal Subgroup of Classical Groups
• Simple Group of Order 60
• Fitting Subgroups
• Index prime power subgroup of simple groups
• 二次剩余
• Equivalent Condition of Semiregular
• Burnside 2-Transitive
• Permutational Isomorphism
• Wedderburn’s little theorem
• https://math.stackexchange.com/questions/2185417/let-r-be-a-ring-and-let-v-denote-the-r-module-r-determine-all-module-h
• Classification of 2-Transitive Groups
• Burnside’s Theorem
• Fusion Classes
• Perfect Field
• 有限域有限扩展是循环的 galois 的
• Minimal Normal Subgroup and Maximal Normal Subgroup
• regular normal subgroup induce a action isomorphic to acting on Omega
• Burnside’s Transfer Theorem
• Clifford Theorem
• Quasisimple
• List of Affine 2-transitive Groups

Done

• List of Almost Simple 2-transitive Group
• “all-or-nothing” lemma
• Mackey Decomposition Formula
• Tensor-Hom Adjunction
• Irreducible element in Gauss Ring
• Separable Extension is Transitive
• p-group has normal subgroup of any prime power order
• Union of the Conjugates of a Proper Subgroup
• Conjugacy Class of An
• GZ-Theorem
• Structure of p-groups
• Normalizer of p-subgroup
• Properties of Finite Field
• Triangle Group
• Sharply Transitive
• Quasisimple Group
• Extraspecial p-groups
• 2-Group with Exponent 2 is Abelian
• Special p-Group
• Algebra
• Group with Cyclic Sylow 2-subgroup
• Radical and Socle of Modules
• Maschke’s Theorem
• Primitive Prime Divisor
• Coset Action

Exercise

• Some Exercises
• zyz’s quiz
• Group of Order 72 with Trivial Center
• Group with Cyclic Sylow Subgroups
• PGL(V) Sharply 3-transitive iff n=2
• Automorphism Groups of Some Groups

Bin

• Fractional Exponents for Complex Numbers

Permutation Group

• Affine Quasiprimitive is Primitive
• Permutation Group Embedded into Holomorph of its Regular Normal Subgroup
• Linear Group with Nontrivial p-Core is Reducible
• [[Holomorph is the Normalizer of $X_R$]]
• Quasiprimitive Group of Type HS, HC and HA are Primitive
• Imprimitive Rank 3 Group is a Wreath Product of two 2-Transitive Groups
• Quasiprimitive Rank 3 are Almost Simple
• Classification of Quasiprimitive Groups
• Equivalent Condition of Primitivity
• Uniqueness of Block System of Imprimitive Rank 3 Group
• Definition of Rank

Finite Geometry

• Finite Geometry
• Partial Geometry
• Partial Linear Space
• Generalized Polygons
• Generalized Quadrangle
• Generalized Octagons
• Generalized Hexagons
• Design
• Strongly Regular Graph

Generalized Polygons

Basic Group Theory

• Sylow Theorems
• Schur Lemma
• NC Lemma
• Except Isomorphisms
• CFSG
• Hall’s Theorems
• Almost Simple Groups
• Group Socle
• Solvable Group
• Composition Series and Principal Series
• Frattini Subgroup
• Frattini’s Argument
• Nilpotent Group
• Normal Subgroups that Intersect Trivially
• Orbits of Normal Subgroups Form a Block System
• Quotient of Commutator is Exactly Abelian

analysis

• Layer Cake Representation