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3. (i) List all the isomorphism types of abelian groups of order 180. [3 marks] (ii) Let G be a group of order 48. Suppo
Posted: Tue Jul 12, 2022 11:39 am
by answerhappygod
- 3 I List All The Isomorphism Types Of Abelian Groups Of Order 180 3 Marks Ii Let G Be A Group Of Order 48 Suppo 1 (63.35 KiB) Viewed 50 times
3. (i) List all the isomorphism types of abelian groups of order 180. [3 marks] (ii) Let G be a group of order 48. Suppose that G acts on a set X with exactly two orbits. Suppose that there are x, y EX such that the order of their stabilisers are G = 24 and Gy 16. Why do x and y belong to different orbits of G? How many elements does X have? [3 marks] (iii) Give an example of a group G of order 48 acting with exactly two orbits on a set with 17 elements. [4 marks]