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group-theory

Generators of a group

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Dₙ as a subgroup of Sₙ Finitely presented groups Free groups Generating sets and Cayley graphs Molecular symmetry and point groups Motivating group actions: groups that move things Necklace and bracelet counting Presentations of D_n and Q_8 revisited Rotations and reflections as generators of Dₙ Symmetry groups of regular polygons, in general Cayley graphs Finitely generated groups Generators of Z_n Group presentations (generators and relations) The dihedral group Dₙ Generators of a group Classification of finite abelian groups Classification of finite cyclic groups Classifying groups of order pq Cyclic subgroups, revisited Greatest common divisor via the Euclidean algorithm Groups of prime order are cyclic Matrix multiplication Quotient groups of cyclic groups Subgroups of cyclic groups Symmetries of a regular n-gon What a graph is Cyclic groups Order of an element Powers and integer exponents of a group element

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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.