Answer to Question #47351 in Abstract Algebra for ayush kumar

Question

(a) Count the number of distinct 3 - cycles in S4. Further, find the number of distinct 4 cycles of length r is Sn, where r>1.
(b) If R is a PID, so is R[x]. True or false ? why ?

(c) Check whether or not '—' is an equivalence relation on Z, where 'a--b if a = br for some n€N'.