Abstract
We call a Y-group a quotient of a Coxeter group with a Y pqr -diagram in accordance with the ATLAS terminology. Here we prove, without computer aid, that some 3-transposition groups are also Y-groups. For each of these groups, the arms of the Coxeter diagram Y pqr are such that (1 = r ≤ q ≤ p ≤ 5) or (2 = r ≤ q ≤ 3, q ≤ p ≤ 5) holds, the additional relations generally describe the center or the Schur multiplier.
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Virotte Ducharme, MM. Some Y-Groups. Geometriae Dedicata 65, 01–30 (1997). https://doi.org/10.1023/A:1004964605735
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DOI: https://doi.org/10.1023/A:1004964605735