Let and be groups, i be the identity element for H, andbe a homomorphism. The kernel of f isis all the elements of G that map to the identity inH. Show that is a subgroup of G.

MATH 242: Elementary Differential Equations Dr. Thi Thao Phuong Hoang Notes from 8/24/17 **Note** I Anything abbreviated with is considered the first prime not to be confused with an exponent Intro 8/24/I7 Differential Equations: Functions – y : R → R | t → y(t) I +ℎ −() Derivative – y (t) : lim →∞ ℎ Definition: A differential equation is a function that relates a function with one or more derivatives Example I: Remarks: I 2 2 a) y = x or = x 1) Only real-value functions can be used I I