Tag Archives: finite

Ways to prove a bijection

Posted on March 17, 2020 by Brent

You have a function and want to prove it is a bijection. What can you do? By the book A bijection is defined as a function which is both one-to-one and onto. So prove that is one-to-one, and prove that … Continue reading →

Posted in logic, proof | Tagged , , , , , , , , | 7 Comments

MaBloWriMo 15: One more fact about element orders

Posted on November 16, 2015 by Brent

I almost forgot, but there is one more fact about the order of elements in a group that we will need. Suppose we have some and we happen to know that is the identity. What can we say about the … Continue reading →

Posted in algebra, group theory, number theory, proof | Tagged , , , , | 1 Comment

MaBloWriMo 14: Element orders are no greater than group size

Posted on November 15, 2015 by Brent

Today we will give an answer to the question: What is the relationship between the order of a group and the orders of its elements? Yesterday, I claimed we would prove that for any element of a group , it … Continue reading →

Posted in algebra, group theory, proof | Tagged , , , , | 2 Comments

MaBloWriMo 13: Elements of finite groups have an order

Posted on November 14, 2015 by Brent

Recall from yesterday that if is a group and is some element of the group, the order of is defined as the smallest number of copies of which combine to yield the identity element. I forgot to mention it yesterday, … Continue reading →

Posted in algebra, group theory, proof | Tagged , , , , | Comments Off on MaBloWriMo 13: Elements of finite groups have an order