() Compute the Cayley table for the group U(12) - (ii) Find the order of each element in the group U(12) (ii) Find the inverse of each element in the group U(12).
0 1 1. Write down the Cayley table for the group generated by the matrices 1 0 -1 0 and 0 1 2. Write down the Cayley table for the permutation group generated by the permutations (12)(34) and (13) in S_4. 3. What do you notice about the two Cayley tables? How do they compare with the Cayley table for Z/8Z? How about the Cayley table for the square?
0 1 1. Write down the Cayley table for the group...
Abstract Algebra I
1. Write down the Cayley table for the group generated -1 0 0 1 by the matrices 1 and 1. 2. Write down the Cayley table for the permutation group generated by the permutations (12)(34) and (13) in S 4 3. What do you notice about the two Cayley tables? How do they compare with the Cayley table for Z/8Z? How about the Cayley table for the square?
1. Write down the Cayley table for the group...
• Let A=1321. Using Cayley-Hamilton theorem compute (a) A-1, (b) p(A) = A5 + A3 +A+1, (c) At
please show step by step
2 Write down the Cayley table for D6/(m3).
11. Let G = Z4 Z4, H = {0,0), (2,0), (0,2), (2,2)). Write the Cayley table for G/H. Is G/H isomorphic to Z4 or Z2 x Z ? Justify your answer. 12. Show that G = {1, 7, 17, 23, 49, 55, 65, 71} is a group under multiplication modulo 96. Then express G as an external and an internal direct product of cyclic groups.
modern algebra
Adventures in Algebra VII: This is completely normal. 2 Write down the Cayley table for D6/(rº).
1. A Cayley diagram and multiplication table for the dihedral group Ds are shown below Section 2 of the class lecture notes describes two algorithms for expressing a group G of order n as a set of permutations in Sn. One algorithm uses the Cayley diagram and the other uses the multiplication table. In this problem, you will explore this a bit further. (a) Label the vertices of the Cayley diagram from the set (1,... ,8) and use this to...
6. (a) Find all of the plane symmetries of the figure below and construct the corresponding Cayley table (b) We say that a group G is abelian if gh hg, Vg, h e G. Is this group of symmetries from part (a) abelian? Justify your answer
6. (a) Find all of the plane symmetries of the figure below and construct the corresponding Cayley table (b) We say that a group G is abelian if gh hg, Vg, h e G....
Question 2 Given the following table, compute the value of ſem f' (e") da T 0 1 e fc) 5 7 10 2 4 9 3 10 0 0 1