Abstract
There are two sequences in two variables which characterize the solvability of finite groups. Namely, the sequence of Bandman, Greuel, Grunewald, Kunyavskii, Pfister and Plotkin which is defined by u 1 = x −2 y −1 x and \({u_{n}=[x u_{n-1}^{-1} x^{-1}, yu_{n-1}^{-1} y^{-1}] }\) and the sequence of Bray, Wilson, and Wilson defined by s 1 = x and \({s_{n}=[s_{n-1} ^{-y}, s_{n-1}] }\). We define new sequences and proof that six of them characterize the solvability of finite groups.
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Communicated by D. Segal.
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Ribnere, E. Sequences of words characterizing finite solvable groups. Monatsh Math 157, 387–401 (2009). https://doi.org/10.1007/s00605-008-0034-6
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DOI: https://doi.org/10.1007/s00605-008-0034-6