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group-theory

Order of an element

taught

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Classification of finite abelian groups Classification of finite cyclic groups Classifying groups of order pq Cyclic subgroups, revisited Generators of a group Groups of prime order are cyclic Quotient groups of cyclic groups Subgroups of cyclic groups When is a direct product cyclic? Consequence of Lagrange's theorem: element order divides… Cyclic groups Order of elements in Z_n and U(n) Orders of elements in a direct product Powers and integer exponents of a group element Order of an element Abelian groups Conjugation External direct products Group actions Group homomorphisms Lagrange's theorem Motivating group actions: groups that move things Order of a group Permutations as bijections Testing whether a structure is a group The Rubik's Cube as a group The group U(n) The group ℤₙ The subgroup test The group axioms Cayley (operation) tables

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