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Back to Symmetry Groups

Problem 1

Avg difficulty 3.0

Let the permutations

α=(1523),\displaystyle\alpha=\begin{pmatrix}1&5&2&3\end{pmatrix}, β=(152)(34),\displaystyle\beta=\begin{pmatrix}1&5&2\end{pmatrix}\begin{pmatrix}3&4\end{pmatrix}, γ=(125)(34), and\displaystyle\gamma=\begin{pmatrix}1&2&5\end{pmatrix}\begin{pmatrix}3&4\end{pmatrix},\text{ and} δ=(1325).\displaystyle\delta=\begin{pmatrix}1&3&2&5\end{pmatrix}.

What is αβγδ\alpha\beta\gamma\delta?

Kan, A Complete Introduction to Abstract Algebra, Groups, Symmetry Groups, Problem 1

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Adapted from A Complete Introduction to Abstract Algebra © 2022–2026 Kan Onn Kit. Licensed under CC BY-SA 4.0. Source: A Complete Introduction to Abstract Algebra. Imported at revision a559e8b.