3. Find the order of each element of the multiplicative group (Z/12Z)*.
Find the order of a=3 in the group (Z,+). Find the order of a=1 in the group (Z,+).
What is the order of an element of a group, find the order of 4 (mod 7). And what is a primitive element mod n, is 5 a primitive element modulo 19? Verify or refute it.
Determine whether the multiplicative group Z∗24 is cyclic or not. Show work to justify your answer.
6. Compute the order of each element in (Z/8Z)* and in (Z/11Z)*.
() 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).
Show that the multiplicative group Z11x is isomorphic to the additive group Z10. Please show me how to find the multiplicative group Z11x
1. If G is any group, and each element of G has order at most 2, show that G is Abelian. Can you find an property? [Hint: For the first part, use the 'shoes-socks property.] example of a group of order 8 with this IC.
In the problems below, give the order of the element in the indicated factor group. (a) in (b) in (c) in (5)(20 points) In the problems below, give the order of the element in the indicated factor group. (a) (1, 2)+ < (1,1) > in Z3 x Z6/ < (1,1) >. (b) (3, 2)+ < (4,4) > in Z6 * Z8/ < (4,4) >. (c) 26+ < 12 > in Z60/ <12>.
5. Prove that a group of order 63 must have an element of order 3.
Just #5 Find the order of every element in EIs. d the rde of every element in the symmetry gronp of thesquare T. What are all of the cyelie sthgroups of the quiatermion group. 0s2 N. Tist all of the cyclic snbgronps of (3 9. Tist eery generator of each sbgroup of order n