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group-theory

Cyclic groups

taught

Taught in

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Required by

Local knowledge map

Local knowledge map

Applying the classification theorem Cayley graphs Classifying groups of prime order Finite abelian groups, revisited Finitely generated groups Group presentations (generators and relations) Simple groups: a first look Small-order classification as a worked recipe The First Sylow Theorem (existence) The dihedral group Dₙ 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 Cyclic groups Consequence of Lagrange's theorem: element order divides… Generators of Z_n Groups of order p² are abelian Internal direct products Lagrange's theorem Order of elements in Z_n and U(n) Orders of elements in a direct product Quotient groups Subgroups generated by a subset Order of an element Powers and integer exponents of a group element The group axioms

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