Answer to Question #188088 in Abstract Algebra for Renu

Question

 a) Using Cayley’s theorem, find the permutation group to which a cyclic group of 

order 12 is isomorphic. (4) 

 b) Let τ be a fixed odd permutation in .

S10 Show that every odd permutation in S is 

10

a product of τ and some permutation in .

A10 (2) 

 c) List two distinct cosets of < r > in ,

D10 where r is a reflection in .

D10 (2) 

 d) Give the smallest n ∈ N for which An is non-abelian. Justify your answer. 

Answer 1

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