Ivan Shishkin, Rye (1878)

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Groups with a single conjugacy class

by Ancient Tree·
24
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This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

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These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Let GG be a group with only one conjugacy class. What can GG be ?

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Solution by Sequoia

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The neutral element ee from GG commutes with any element of GG, hence it is the only element that belongs to its conjugacy class. So GG has to be equal to {e}\{e\}.

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