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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2006 • Question 3

Question

Math 6310 • Algebra Fall 2006 • Question 3

Describe the structure of a Sylow 2-subgroup of the symmetric group \(S_n\) in terms of products and semidirect products of known groups for:

  1. \(n=4\); and
  2. \(n=8\).

Raw LaTeX

Describe the structure of a Sylow 2-subgroup of the symmetric group \(S_n\) in terms of products
and semidirect products of known groups for:
\begin{enumerate}
\item[(a)] \(n=4\); and
\item[(b)] \(n=8\).
\end{enumerate}

Topic Tags

Normal Subgroups and Commutator Subgroups Sylow Theorems Symmetric and Alternating Groups Tensor Products of Modules