• Want FREE Counselling for Exam Preparation?
###### Call Us
800-355-2211

Speak With a Friendly Mentor.

###### Deepika posted an Question
April 22, 2022 • 14:08 pm 30 points
• UGC NET
• Computer Science & Applications

# What is group

• 0 Likes
• 0 Shares
• ##### Aparna 1

A group is a finite or infinite set of elements together with a binary operation (called the group operation) on that set that together satisfy the fundamental properties. 1. Closure 2. Associativity 3. Identity property and 4. Inverse property. Suppose, G be a non-void set with a binary operation * that assigns to each ordered pair (a, b) of elements of G an element of G denoted by a * b. We say that G is a group under the binary operation * if the following three properties are satisfied: 1) Associativity :- The binary operation * is associative i.e. a*(b*c)=(a*b)*c , ∀ a,b,c ∈ G 2) Identity :- There is an element e, called the identity, in G, such that a*e=e*a=a, ∀ a ∈ G 3) Inverse :- For each element a in G, there is an element b in G, called an inverse of a such that a*b=b*a=e, ∀ a, b ∈ G

TQ mam

sub group means

Best Wishes for study and NET Exam

Subgroup :- Let H be a nonempty subset of a group G. If H also becomes a group under the same binary operation (*) as in G, then H is called as a subgroup of G. We use the notation H < =G to indicate that H is a subgroup of G. A subgroup H is a subset of a group G (denoted by H < =G ) if it satisfies the four properties simultaneously -Closure, Associative, Identity, Inverse

### Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

• Updated Syllabus, Paper Pattern & Full Exam Details
• Sample Theory of Most Important Topic
• Model Test Paper with Detailed Solutions
• Last 5 Years Question Papers & Answers