Equivalence Relation

Binary Operation

Commutative

Associative

Binary Algebraic Structure

Identity Element

Isomorphism

Group

Abelian

Left and Right
Cancellation Laws

Subgroup

Cyclic Subgroup
of G generated by a

Cyclic Group

Order of a cyclic subgroup

Permutation of a set

Symmetric Group

Alternating Group

Left and Right Cosets

Index
(G : H)
of H in G

Homomorphism

Normal

Simple

Factor (Quotient) Groups