MATH 2120 Lecture 17: 2120 Notes2015.11.17

Recursion Question 5. In the following question, you will be asked to program the following using recursion. If you have an iterative solution, you may use it, but the most you can get for the question will be half credit. (5) points) Consider the following mathematical function h which operates on integers. (1, if n < 2 h(n) = n(n-1) +n if n > 2 and n is even han -2) +2*n if n > 2 and n is odd In Java, use recursion to write a method h which takes as input an int n and returns h (n). public static int h(int n) {

Let H ba a subgroup of a group G and let N(H) be its normalier,Prove that

a)H is a normal subgroup of N(H)

b)If H is a normal subgroup of a subgroup K of G, then K is subset of N(H).