abstract algebra
Not what you're looking for?
Let M and N be two Normal subgroups of G. Prove that
(1) MN=NM
(2) MN is a normal subgroup of G
(3) if M ^ N = {e} then MN/N and M are isomorphic ( ^ means "and")
Thank you
Purchase this Solution
Solution Summary
This solution is comprised of a detailed explanation to answer abstract algebra.
Solution Preview
Proof:
(1) For each element in MN, it has form mn, where m is in M and n is in N.
Since N is normal, then mnm^(-1) is in N. So mn = (mnm^(-1))m is in NM. Thus MN is a subset of NM.
For each element in NM, it has form nm, where n is in N and m is in M.
Since M is normal, then nmn^(-1) is in M. So nm = (nmn^(-1))n is in MN. Thus NM is a ...
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.