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Section Definitions and Algorithms

This page contains definitions of important terms and algorithms used throughout the course.

Subsection Definitions

Definition 4 Symmetry
Definition 10 Binary Operation
Definition 11 Abelian group
Definition 15 Subgroup
Definition 20 Center of a Group
Definition 23 Order of a Element
Definition 25 Cyclic Group
Definition 30 Cyclic Subgroup
Definition 34 Permutation
Definition 35 Permutation Group
Definition 36 Symmetric Group
Definition 44 Cycle Type of a Permutation
Definition 48 Group Isomorphism
Definition 49 Alternating Group
Definition 57 Automorphism of a Group
Definition 59 Cosets of a Subgroup
Definition 64 Inner Automorphism
Definition 76 External Direct Product of Groups
Definition 87 Normal Subgroup
Definition 91 Quotient Group
Definition 97 Group Homomorphism
Definition 98 Kernel of a Homomorphism
Definition 116 Group Action

Subsection Algorithms