Purchase Solution

The solvability of some quotient group

Not what you're looking for?

Ask Custom Question

Hello everyone, here's a problem I need help with!

Let G be a group, and let K be a subgroup of G.

If K_i is normal to G, for each i = 1, 2, ..., n,
write K = K_1 (intersect) K_2 (intersect) ... (intersect) K_n.

THE QUESTION: If G / K_i is solvable for each i, show that G / K is solvable.

I'm sorry if it's hard to read, so I've attached a copy of the question as an image, just in case.
Thanks for your time.

Purchase this Solution

Solution Summary

It is proved that if the quotient of a group by each of the given normal subgroups is solvable, then the quotient of this group by the intersection of these subgroups is also solvable, provided that the number of subgroups is finite.

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

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.

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