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group-theory

The subgroup test

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Collapsing cosets into elements Coset representatives and the coset partition Cyclic subgroups, revisited Generator matrices and syndrome decoding Group theory in computer science and coding Index of a subgroup Normal subgroups Subgroups generated by a subset Subgroups of cyclic groups The subgroup lattice When left and right cosets agree Intersections of subgroups Left and right cosets Linear codes as subgroups of (F_2)^n Products of subgroups Subgroups generated by a subset The finite subgroup test The subgroup test Abelian groups Conjugation Equivalence relations External direct products Group actions Group homomorphisms 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 group axioms Cayley (operation) tables

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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.