Introduction to elementary group theory

Introduction:Group theory is the study of algebraic structures called groups. This theory will rely heavily on set theory and modular arithmetic as well . It will require an understanding of mat...

Binary Operation, Operation Table and Congruent Modulo

Elementary Group TheoryBinary Operation:f: S ⊗ S → S, S is any set.  f: Q ⊕ Q → Q, Q is a set of rational numbers.f: Z ⊕ Z → Z, Z is a set of integers.⊗, ⊕, ౦, x, -, +, ∗ are notations of binary op...

Algebraic Structure and Group

Algebraic StructureA set together with a binary operation gives rise to what is known as an algebraic structure.Given a, b, c as the elements of the set G, the algebraic structure (G,*) maybe:Close...

Elementary Properties of a Group

Elementary Properties of a Group Theorem I: The identity element in a group (G,౦) is unique.Proof:Let e and e’ be two identity elements in a group (G,౦), if possible.Then, When e is the identity e...

Group with elements other than numbers

a) Permutation Group:A permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G. A Permutation group elem...

Group ,its axiom and types

Group:An algebraic structure (G,*) , where G is a non- empty set with an operation '*' defined on it, is said to be a group  , if the operation * satisfies the following axioms.Closure axiom : G i...

Urine formation

Process of Urine formationThe basic filtration units are the nephrons. Each kidney has a million Nephrons packed together.Urine formation occurs in three steps:1.   Filtration2.   Reabsorption3.   ...