Answer to Question #47349 in Abstract Algebra for ayush kumar

Question

(a) Let G be a group of order 21. Show that G has a proper normal non-trivial subgroup.

(b) Apply the principle of induction to show that n3 + (n + 1)3 + (n + 2)3 is divisible by 9 V nEN.

(c) State the Fundamental theorem of Algebra. Also give a polynomial of degree n over a ring R which has more than n roots in R.