30 points
>
Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
What is a symmetric group give me some examples
what is a symmetric group give me some examples and also tell it's importance.
1 Answer(s)
Answer Now
- 0 Likes
- 3 Comments
- 0 Shares
-
![comment-profile-img]()
>
-
Anuj s.
Definition and Basic Properties of Symmetric Group Let X_n = \{1,2,\ldots,n\}.X n ={1,2,…,n}. Then S_nS n is the set of bijections \sigma \colon X_n \to X_n.σ:X n →X n . Since the composition of two bijections is a bijection, composition is a binary operation on S_n,S n , which turns it into a group. The identity element of the group is the identity function ii: i(k) = ki(k)=k for all k \in X_n.k∈X n . The order of the group S_n,S n , the number of permutations on nn objects, is n!.n!. See the permutation wiki for a discussion. S_nS n is non-abelian for n\ge 3.n≥3. For a proof, see example 5 in the group theory wiki exercises. S_3S 3 is the smallest non-abelian group, of order 3!=6.3!=6.
-
Anuj s.
Symmetric Group The symmetric group S_nSn is the group of permutations on nn objects. Usually the objects are labeled \{1,2,\ldots,n\},{1,2,…,n}, and elements of S_nSn are given by bijective functions \sigma \colon \{1,2,\ldots,n\} \to \{1,2,\ldots,n\}.σ:{1,2,…,n}→{1,2,…,n}. The group operation on S_nSn is composition of functions. The symmetric group is important in many different areas of mathematics, including combinatorics, Galois theory, and the definition of the determinant of a matrix. It is also a key object in group theory itself; in fact, every finite group is a subgroup of S_nSn for some n,n, so understanding the subgroups of S_nSn is equivalent to understanding every finite group
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
Sign Up to Download FREE Study Material Worth Rs. 500/-
Deepak singh 1 Best Answer
Symmetric groups are collection of bijection functions . See attachment and go through this video for better understanding. https://youtu.be/yo5Bu33pVBE