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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2005 • Question 8

Question

Math 6310 • Algebra Fall 2005 • Question 8

Let \(K\) be a finite field.

  1. Show that \(|K|=p^n\) for some prime \(p\).
  2. Show that \(K^*=K-\{0\}\) is a cyclic group with respect to multiplication.

Raw LaTeX

Let \(K\) be a finite field.
\begin{enumerate}
\item[(a)] Show that \(|K|=p^n\) for some prime \(p\).
\item[(b)] Show that \(K^*=K-\{0\}\) is a cyclic group with respect to multiplication.
\end{enumerate}

Topic Tags

Abelian Groups and Direct Sum Decompositions Finite Fields Finite Group Theory