Abstract Algebra: Theory and Applications · Problem 9.4.4

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-proof

Problem

Prove that U(8)U(8) is isomorphic to the group of matrices (1001),(100−1),(−1001),(−100−1).\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}, \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}, \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}.

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