Let f : G H be a homomorphism of groups. Let ker(f): = {g G|f(g)
Fantastic news! We've Found the answer you've been seeking!
Question:
Let f : G → H be a homomorphism of groups. Let
ker(f): = {g ∈ G|f(g) = e}
where e ∈ H is the identity of H.
(a) Show that ker(f) is a subgroup of G. (ker(f) is called the kernel of f).
(b) Show that ker(f) is a normal subgroup.
(c) Show that f is injective if and only if kerf(f) = {e}
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date: