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Previous problem in #7 is question #6. 7. Cosets in Dihedral Groups. [Purpose:...

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Previous problem in #7 is question #6.

7. Cosets in Dihedral Groups. [Purpose: practice creating cosets + have examples to illustrate concepts] Repeat the previous problem, this time using G=D3 and H being the cyclic subgroup generated by R. 6. Cosets in Dihedral Groups. [Purpose: practice creating cosets + have examples to illustrate concepts] Let G be the dihedral group D3, and let H be the cyclic subgroup generated by F. (a) Before calculating any cosets, how many elements will be in each coset and how many different cosets will there be? (b) Find all the different left cosets of H. (Write each coset in roster notation.) (c) Repeat for the right cosets. (A right coset is Ha, the set of elements you get by multiplying each element of H with a on the right instead of left.) (d) Do the left and right cosets determine the same partition of G

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