Purchase Solution

Non-Identity Elements of Prime Order

Not what you're looking for?

Ask Custom Question

Suppose G is a finite group with the property that every non-identity element has prime order (D3 and D5 are examples of groups with this property). Show that if the center of G, Z(G), is not trivial, then every nonidentity element of G has the same order.

Purchase this Solution

Solution Summary

Non-Identity Elements of Prime Order are investigated.

Solution Preview

Proof:
we select two arbitrary nonidentity elements x and y in G. Suppose the order of x is p and the order of y is q. From the condition, p and q are prime numbers. We have the following 3 cases.
Case 1: Both x and y are in Z(G), then xy=yx. Suppose the order of xy is r, then we have
...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

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.