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group-theory

Quotient groups

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Classifying groups of order pq Small-order classification as a worked recipe Solvable groups The Correspondence Theorem The Jordan-Hölder theorem The Schur–Zassenhaus theorem The Second Isomorphism Theorem (groups) The Third Isomorphism Theorem (groups) A first look at the First Isomorphism Theorem Abelianization Constructing a composition series Group extensions (introduced) Groups of order p² are abelian Quotient groups of cyclic groups Quotient groups of permutation groups The First Isomorphism Theorem (groups) The quotient construction as a recurring pattern Quotient groups A first look at semidirect products Characteristic subgroups Cyclic groups Groups of prime order are cyclic Internal direct products Kernel of a homomorphism Normal subgroups: examples and counterexamples Normality tests (generators, index 2) Simple groups: a first look The alternating group Aₙ The center of a group The commutator subgroup The conjugation action and conjugacy classes The normalizer of a subgroup The orbit-stabilizer theorem The symmetric group Sₙ Well-definedness of coset multiplication Normal subgroups Conjugation Left and right cosets

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.