Order of permutation

Binary operation
Associative
Commutative

Stabilizer of s in G

Group

Zero divisor
&
Unit in R

Sylow's Theorem (formal)

Transposition (cycles)

Symmetric group on the set Omega

Permutations of Omega

Third Isomorphism Theorem (groups)

Unique Factorization Domain (U.F.D)

Subgroup of G generated by A

Subring

Subgroup

Sylow Theorem

Sum, Product, Power of Ideals I

Solvable groups

Sign of sigma
Even and Odd Permutations

Simple groups

Second isomorphism theorem (groups)

Relations

Quotient group or Factor group

Quotient Ring

Ring

Second Isomorphism Theorem for Rings

Presentation of G

Principal Ideal Domain (P.I.D)

Prime Ideal

Quaternion Group Q_8

P-groups
&
Sylow p-subgroups

Orbit of G
&
Transitive action

Order (element)

Norm
&
Positive Norm

Natural Projection (homomorphism)
of G onto G/N

Normalizer of A in G

Length of a Cylce

Lattice of Subgroups of Q_8

Left and Right Cosets

Maximal Ideal

Left, Right, Two-sided Ideal

Lattice of D_8

Lagrange's Theorem

Lattice of S_3

Klein 4 Group

Lattice of D_16

Integral Domain

Kernel of a Homomorphism \rho

Kernel of an Action

Isomorphism

Irreducible, Prime, and Associate element

Homomorphism (groups)

Inner automorphism

Index of H in G

Ideal generated by A

Field

First Isomorphism Theorem (groups)

Group Action

First Isomorphism Theorem for Rings

Fourth Isomorphism Theorem (Groups)

Euclidean Domain

Division Ring

Fibers of \rho

Cycle type of \sigma
&
Partition of n

cyclic group

Cycle decomposition of \sigma

Conjugate (element , set)
&
Normal group

Conjugate (subsets)

Conjugate (elements)

Class Equation

Binary operation

Cauchy's Theorem

Cayley's Theorem

Cycle

Composition Series

Center of G

Characteristic in G

Centralizer of A in G

Alternating group

Automorphism of G

Alternating Group Example