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group-theory

Groups of order p² are abelian

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Classifying groups of order pq Small-order classification as a worked recipe Groups of order p² are abelian A first look at the First Isomorphism Theorem Abelianization Classifying groups of prime order Constructing a composition series Group extensions (introduced) Group theory and graph theory: connections Inner automorphisms Internal direct products Nilpotent groups Quotient groups of cyclic groups Quotient groups of permutation groups Simple groups: a first look Sylow p-subgroups The First Isomorphism Theorem (groups) The First Sylow Theorem (existence) The Second Sylow Theorem (conjugacy) The quotient construction as a recurring pattern Groups of prime order are cyclic Quotient groups The center of a group The conjugation action and conjugacy classes The orbit-stabilizer theorem Conjugation Consequence of Lagrange's theorem: element order divides… Cyclic groups Group actions Lagrange's theorem Normal subgroups Orbits and stabilizers

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