Basic set theory
Set
Methods of representing set
Types of sets
Subsets
Operations on sets
General properties of sets
Modular arithmetic
Relation of congruence modulo n in the set of integers
Addition modulo of a positive integer n
Multiplication modulo of a positive integer n
Divisibility in the set of integers
Greatest common divisor
Relatively prime integer
Prime integer
Congruence relation
Residue classes modulo n
Algebra of residue classes
Linear congruence
Permutation
Symbol
Equality of two permutations
Identity permutation
Product or composition of permutations
Properties of permutations
Transformation groups
Orbit of a permutation
Circular or cyclic permutation
One-row symbol
Length
Disjoint cycles
Transposition
Inversions
Even & odd permutations
Alternating set
Alternating group
Regular permutation group
Group theory
Binary operation
Algebraic structure
Group
Groupoid
Semi group
Monoid
Abelian group
Finite & infinite groups
Order of a group
Properties of group
Multiplication & addition tables
Group table
Integral power of an element
Order of an element of a group
Cyclic group
Properties of cyclic groups
Subgroups
Complex
Subgroups
Improper & proper subgroups
Algebra of complex of a group
Criterion for a complex to be a subgroup
Algebra of subgroups
Cyclic group
Properties of cyclic groups
Cyclic subgroups
Co-sets
Properties of co-sets
Co-set decomposition
Transform
Index of subgroups in a group
Euler function
Normal subgroups
Simple group
Hamiltonian group
Conjugate elements
Self conjugate elements
Conjugate class
Conjugate subgroups
Self conjugate subgroups
Conjugate class of a subgroup
Centrariser or normalizer
Normalizer of a subgroup of a group
Class equation of a group
Centre of a group
Quotient groups
Homomorphism
Homomorphism
Types of homomorphism
Kernel of homomorphism
Isomorphism of groups
Automorphism
Inner automorphism
Automorphism groups
Ring theory
Ring
Types of rings
Properties of a ring
Subrings
Integral domain
Subdomain
Ordered integral domain
Characteristic of a ring
Field
Subfield
Prime field
Homomorphism
Ring homomorphism
Ring isomorphism
Kernel of a ring homomorphism
Ideals
Types of ideals
Properties of ideals
Algebra of ideals
Quotient rings
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