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Lectures on Group Theory

In: Papers on Group Theory and Topology

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  • Max Dehn

Abstract

We begin our considerations with the generation and geometric representation of the group Σ3! of permutations of three things. We have already shown that this group may be generated by a transposition s1, which exchanges the first and second terms, and a cyclic permutation s2 of all three terms, which replaces the first element by the second, the second by the third, and then the third by the first. When we apply the transposition s1 twice, or the cycle s2 three times, then in each case we come back to the identity, hence $$ \text{s}_\text{1}^\text{2} = 1\text{ and s}_\text{2}^\text{3} = 1. $$

Suggested Citation

  • Max Dehn, 1987. "Lectures on Group Theory," Springer Books, in: Papers on Group Theory and Topology, pages 5-46, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4668-8_2
    DOI: 10.1007/978-1-4612-4668-8_2
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