From Herstein's Abstract Algebra. Section 2.7 #7
If φ is a homomorphism of G onto G' and N ◅ G, show that φ(N) ◅ G.
Attempt:
I want to prove that if k ∈ G' then kφ(N)k-1 = φ(N), but k = φ(n) for some n... then idk what.
I'm not 100% clear on what your question is. If the question is asking what are the chances that you will have two instances of heads in your first two flips out of 6 flips you simply need to do:
\frac{1}{2} * \frac{1}{2}
(50% chance of heads...
Homework Statement
Find all elements x in S4 such that x4 = e.
(e is the identity)
Homework Equations
Cycle notation is advised.
The Attempt at a Solution
I know there are 4 elements in this (1 2 3 4). And I feel like I need to find the order of S which can be found by finding the number...