Let Sn be the group consisting of the set of all permutations on n letters, together with the operation of composition. Let Cn be the subset of Sn consisting of the identity and all cycles of length n. a) What is |Cn|? Be careful-the answer is not n + 1. b) Show that C3 is a subgroup of S3. c) Show that C4 is not a subgroup of S4. d) For which values of n is Cn a subgroup of Sn? Prove your answer.

Let Sn be the group consisting of the set of all permutations on n letters, together with the operation of composition. Let Cn be the subset of Sn consisting of the identity and all cycles of length n. a) What is |Cn|? Be careful-the answer is not n + 1. b) Show that C3 is a subgroup of S3. c) Show that C4 is not a subgroup of S4. d) For which values of n is Cn a subgroup of Sn? Prove your answer.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 38E: Let n be appositive integer, n1. Prove by induction that the set of transpositions...

See similar textbooks