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11 Nov 2019
» Notations: Gn is the group of invertible congruence classes mod n. D(n) is the group of symmetries of a regular polygon with n vertices. S(n) is the symmetric group on n symbols. i.e., the group of permutations of {i. . . . , n} 1. Consider the group D(4) (it was described in problem 1 of Hw 11) In (a, b, c), determine weather the given subset H of D(4) is a subgroup is a subgroup, just answer Yes; if it is not, answer No and explain why (b) H-{id, Ri ) (c) H-{id, R1, R2, R3, R4\ (d) What is the order of p? (e) List all elements in the subgroup ãÏã generated by Ï (f) Is the group D(4) cyclic? Justify your answer
» Notations: Gn is the group of invertible congruence classes mod n. D(n) is the group of symmetries of a regular polygon with n vertices. S(n) is the symmetric group on n symbols. i.e., the group of permutations of {i. . . . , n} 1. Consider the group D(4) (it was described in problem 1 of Hw 11) In (a, b, c), determine weather the given subset H of D(4) is a subgroup is a subgroup, just answer Yes; if it is not, answer No and explain why (b) H-{id, Ri ) (c) H-{id, R1, R2, R3, R4\ (d) What is the order of p? (e) List all elements in the subgroup ãÏã generated by Ï (f) Is the group D(4) cyclic? Justify your answer