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group-theory

The orbit-stabilizer theorem

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Local knowledge map

Local knowledge map

Small-order classification as a worked recipe The Second Sylow Theorem (conjugacy) The Sylow theorems Group theory and graph theory: connections Groups of order p² are abelian Sylow p-subgroups The First Sylow Theorem (existence) The orbit-stabilizer theorem Burnside's lemma Classification of finite abelian groups Classifying groups of order pq Consequence of Lagrange's theorem: element order divides… Euler's theorem, proved via Lagrange Fixed points of a group element Groups of prime order are cyclic Possible orders of elements and subgroups Quotient groups Reading group structure from a Cayley graph Stabilizers of a group action The center of a group The conjugation action and conjugacy classes Transitive and faithful actions p-groups Lagrange's theorem Orbits and stabilizers Group actions Index of a subgroup

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