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)
Deepak Patra posted an Question
November 24, 2021 • 14:02 pm
![]()
30 points
30 points
- IIT JAM
- Mathematics (MA)
47. express aut(u(25) in the form z,, dz, 48. determine aut(z, z,). 40 sunnase that n n. are nositie even inted
47. Express Aut(U(25) in the form Z,, DZ, 48. Determine Aut(Z, Z,). 40 Sunnase that n n. are nositie even inted
1 Answer(s)
Answer Now
- 0 Likes
- 1 Comments
- 0 Shares
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/-
Anonymous User![best-answer]()
check attachment 48 Z2+Z2=⟨(0,1),(1,0)⟩=⟨(1,0),(1,1)⟩=⟨(1,1),(0,1)⟩and these are only only generators with minimum no. of elements Now f is a automorphism on Z2×Z2 iff f sends any of these three basis-sets to another basis-sets. i.e. we have 3 choices of a basis-set to be image of f .Also for any of these choices we have 2 choices to pick a particular value of a element.i. e there are 6 automorphism(for example Consider f((0,1),(1,1))=(0,1),(1,0) . The RHS can be chosen 3 ways and each case can be done for 2 ways for f((0,1))=(0,1)or (1,0)) So|Aut(Z2×Z2)|=6 Also note that the maximum order of a element this group is 3 i.e Aut(Z2×Z2)≅S3
48) ????
plz wait
check 48