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- $|a|$ and $|G|$ - Order For Elements and Groups
- $A_n$ - Alternating Group of Degree $n$
- $Z(G)$ - Center Of A Group
- Abelian Group
- A Closed Set Of Permutations
- Affine Encryption Key
- Algebraic Number
- Associates Irreducibles Primes
- Automorphism Of A Colored Directed Graph
- Automorphism Of A Graph
- Automorphisms And Inner Automorphisms
- Binary Operation
- Cayley Graph Of A Group
- Cayley Graph Of A Span Of Permutations
- Centralizer Of An Element
- Characteristic Of A Ring
- Commutative Ring
- Composition Combination Of Permutations
- Conjugacy Class Of A
- Content Of A Polynomial Primitive Polynomial
- Cosets $Ha$ and $aH$
- Cyclic Group
- Definition.The image of a function $f(A)$
- Degree Of A Polynomial
- Disjoint Cycle Notation
- Encryption Key
- Equivalence Relation
- Extension Field
- External Direct Products $G\times H$ or $G\oplus H$
- Factor Group or Quotient Group of $G$ by $N$, or $G/N$
- Factor Ring
- Field
- Gaussian Integers
- Group
- Group Homomorphism
- Group Isomorphism
- Ideal
- Ideal Generated By $a_1, \ldots, a_n$, or $\left<a_1,a_2,\ldots,a_n\right>$
- Idempotent And Nilpotent
- Identification Graph Using Cosets
- Index of $H$ in $G$, or $|G:H|$
- Integer Linear Combination Of Integers
- Integral Domain
- Internal Direct Product Of Two Subgroups
- Intersection Of A Collection Of Sets
- Irreducible Polynomial Reducible Polynomial
- Isomorphic Graphs
- Kernel Of A Homomorphism
- Kernel Of A Ring Homomorphism
- Modular Multiplicative Inverse and $U(n)$
- Modular Arithmetic
- Normal Subgroup $N\trianglelefteq G$
- Permutation
- Polynomial Rings Over A Field
- Polynomial Ring With Coefficients In R
- Preimage Or Inverse Image
- Prime Ideal And Maximal Ideal
- Principal Ideal Domain PID
- Principle Ideal Generated by $a$, or $\left<a\right>$
- Ring
- Ring Homomorphism And Isomorphism
- Semigroup And Monoid
- Simple Shift Permutation Of The Alphabet
- Special Linear Group $\text{SL}(m,\mathbb{Z}_n)$
- Subgroup
- Subgroup Generated By An Element
- Subring
- Symmetric Group on $X$
- The Dihedral Groups $D_{n}$
- The Game of Permutation Scoring also called Generate/Don't Generate
- The Set $\mathbb{Z}_n$ Of Integers Mod $n$
- The set product $HK$
- The Subgroup $n\mathbb{Z}$
- The Euler Phi Function
- The Order Of A Permutation
- The Product Of A Set And An Element
- The Subgroup Generated By A Subset
- Unique Factorization Domain
- Unity And Unit
- Zero Divisor