Please Login to access more options.

Problem 41 (The Order Of A Finite Field)

Suppose that $F$ is a finite field of characteristic $p$. Show that the order of $F$ must be $p^n$ for some integer $n$.

Click for a hint.

What's the additive order of every element in $F$? Use the fundamental theorem of finite Abelian groups, and just pay attention to the additive group, ignoring completely the multiplicative part of $F$.

The following pages link to this page.

Problem.TheOrderOfAFiniteField
Schedule.20140129
Schedule.20140131
Schedule.20170201
Schedule.20170203
Schedule.20170208
Schedule.20170213
Schedule.AllProblems442

Edit
Page History
Source
Attach File
Backlinks
List Group

Page last modified on January 31, 2017, at 12:30 PM

Big View Home Login Edit History Recent Changes
HomePage Current Problems All Problems Pictures ProblemsByWeek List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Problem The Order Of A Finite Field Please Login to access more options. Problem 41 (The Order Of A Finite Field) Suppose that $F$ is a finite field of characteristic $p$. Show that the order of $F$ must be $p^n$ for some integer $n$. Click for a hint. What's the additive order of every element in $F$? Use the fundamental theorem of finite Abelian groups, and just pay attention to the additive group, ignoring completely the multiplicative part of $F$. The following pages link to this page. Problem.TheOrderOfAFiniteField Schedule.20140129 Schedule.20140131 Schedule.20170201 Schedule.20170203 Schedule.20170208 Schedule.20170213 Schedule.AllProblems442 Edit Page History Source Attach File Backlinks List Group Page last modified on January 31, 2017, at 12:30 PM
skin config pmwiki-2.2.142