4) (5 marks) List all of the subgroups of Z24. List all of the generators of...
Consider Z3s. Find all generators for Z3s. List all subgroups of Z36, and find all inclusions between subgroups (or draw the lattice). For what integers a does the map a:Z36- Zz defined by va:x H ya extend to a homomorphism? Why? Can a ever be surjective? Explain
(a) List all the generators of < 5 > in Z60. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60. 7. (7 points each) (a) List all the generators of <5> in Z6o. (b) List all of the left cosets of <10 > in the subgroup < 2 > of Z60-
(a) List all the generators of < 5 > in Z6o. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60.
4. (a) (3 points) List all the subgroups of the symmetric group S3. (b) (4 points) List all the normal subgroups of Sz. (c) (3 points) Show that the quotient of S3 by any nontrivial normal subgroup is a cyclic group.
Consider the additive group ℤ(20). (a) How many subgroups does ℤ(20) have? List all the subgroups. For each of them, give at least one generator. (b) Describe the subgroup < 2 > ∩ < 5 > (give all the elements, order of the group, and a generator). (c) Describe the subgroup <2, 5> (give all the elements, order of the group, and a generator).
Order and Cyclic Subgroups: Problem 5 Previous Problem Problem List Next Problem (1 point) Let x be an element of order 91 in a group G (not necessarily cyclic, finite, or Abelian). How many distinct subgroups of G are contained in (x)?
Question 1 (25 marks) For a large aircraft with more than one generators, all generator electric outputs must be synchronized on the power buses. Indicate how many parameters those affect the synchronization of AC and DC multi-generator system. Briefly describe the system or the method used to control the parameters. (25 marks)
1. 2. Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw its lattice diagram If α : G → C6 is an onto group homomorphism and \ker(a)-3, show that \G\ = 18 and G has normal subgroups of orders 3, 6 and 9. Use the Correspondence Theorem to find all subgroups of S that contain K = {1, (12)(3 4), (13)(2 4), (1 4)(2 3)], Draw...
5. Suppose H and K are subgroups of G and H 10, and |K-21. Prove that 6. Consider the subgroup <3 > of Z12. Find all the cosets of < 3>. How many distinct cosets are there?
Table 2 shows a list of 10 generators which have submitted offers for supplying electricity and their prices Table 2. List of generators and their details GeneratorMin Generation Max GenerationPrice (E/MWh) Number 2 4 300 1000 300 800 250 200 500 320 500 200 1200 20.5 100 20 17 5 50 200 80 100 10 25 7 27 15 12 10 (i) Arrange the generators in merit order Determine which generators would be called upon to supply with the predicted...