If A and B are subsets of a group G, define
AB = {ab | a 2 A, b 2 B}. Now suppose phi: G -> G0 is a homomorphism of groups and N = Ker(phi) is its kernel.
(i) If H is a subgroup of G, show that HN = NH. (Warning: this is an equation of sets; proceed
accordingly; do not assume that G is abelian.)
(ii) Show that phi-inverse[phi[H]] = HN.
Thanks.
Solution Summary
Kernels and Homomorphisms are investigated. The solution is detailed and well presented.
...Homomorphisms and kernels are investigated ... mapping defined is a homomorphism and in that case in which it is homomorphism, determine the Kernel: G is ...
Group Theory : Homomorphisms, Kernels, Isomorphisms and Fields. ... (b) If h: G1 ?> G2 is a homomorphism, define the kernel of h.Prove that the range of h is ...
... Let f: *  + be defined by f(z)= |z|. Prove that f is a homomorphism and find the kernel of f. Please see the attachment. ...
Kernel of Phi and Homomorphism. Let phi is a homomorphism from Z30 onto a group order 3. Determine the kernel of phi. Find all generators of the kernel of phi. ...
... Є S | akk=0} is the kernel of f d ... C-->M2(R) a+bi -->[ab] is an interjecting homomorphism. ... Commutative Rings, Ideals, Kernels, Matrices and Injective and ...
... a) (the integers modulo 2 with the operation), (mod 2). This is a group homomorphism since The kernel of is the subgroup and the image of is (please see the ...
... Definition: ker f = {g in G | f(g) = e}] But the kernel of a homomorphism is trivial (consists only of the identity element) if and only if it is injective. ...
... Please see attached file. This shows how to find formulas for group homomorphisms, and how to find kernel and image. Homomorphism Problem 2: Solution: ...
