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group-theory

Conjugation

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Characteristic subgroups Constructing a composition series Group extensions (introduced) Groups of order p² are abelian Internal direct products Nilpotent groups Normal subgroups: examples and counterexamples Normality tests (generators, index 2) Outer automorphisms (introduced) Quotient groups Simple groups: a first look The Second Sylow Theorem (conjugacy) The Third Sylow Theorem (counting) The commutator subgroup Well-definedness of coset multiplication Inner automorphisms Normal subgroups The center of a group The conjugation action and conjugacy classes The normalizer of a subgroup Conjugation Abelian groups Automorphisms External direct products Group actions Group homomorphisms Left and right cosets Motivating group actions: groups that move things Order of a group Order of an element Permutations as bijections Testing whether a structure is a group The Rubik's Cube as a group The group ℤₙ The subgroup test The group axioms Cayley (operation) tables

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