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Journal Article

Homophonic quotients of free groups. (Quotients homophones des groupes libres.)


Schoof,  René
Max Planck Society;

Washington,  Lawrence
Max Planck Society;


Zagier,  Don
Max Planck Institute for Mathematics, Max Planck Society;

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Mestre, J.-F., Schoof, R., Washington, L., & Zagier, D. (1993). Homophonic quotients of free groups. (Quotients homophones des groupes libres.). Experimental Mathematics, 2(3), 153-155.

Cite as: http://hdl.handle.net/21.11116/0000-0004-3905-7
The authors consider the group on the 26 generators a,b, c,\dots, z, the letters of the Latin alphabet and relations A=B where A, B are words with the same pronunciation in the English language (corr. the French language). The paper is bilingual, the French language for the English case and the English language for the French case. They prove that in either case the group G is trivial. They comment that the German case has been proved recently by Herbert Gangl (the group G is still trivial). On the other hand the analogously defined group for Japanese (written in katakama) is free on 46 generators. The reviewer adds that the group G, defined analogously in Greek, is free on the six generators δ, ζ, θ, ξ, χ, \psi. The authors generalizes their result by considering an extra generator, a space in the English case, or accented letters in the French case and prove that their group is still trivial.