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Certain cyclically presented groups are isomorphic. (English) Zbl 0932.20034

For all \(n\geq 1\) the two cyclically presented groups \[ G_1(n)=\langle x_i\mid x^{-1}_{i+1}x_{i+2}x^{-1}_{i+1}x_{i+2}x_ix^{-1}_{i+1}x_i=1\rangle_n \] and \[ G_2(n)=\langle y_i\mid y^{-1}_{i+1}y_{i+2}y_iy^{-1}_{i+1}y_{i+2}y^{-1}_{i+1}y_i=1\rangle_n \] are isomorphic.

MSC:

20F05 Generators, relations, and presentations of groups

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References:

[1] DOI: 10.1017/CBO9780511629259.040 · doi:10.1017/CBO9780511629259.040
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[6] DOI: 10.1006/jsco.1994.1007 · Zbl 0824.20020 · doi:10.1006/jsco.1994.1007
[7] Rolfsen Dale, Mathematics Lecture Series 7 (1976)
[8] Takahashi Moto-o, Tsukuba J. Math 13 pp 175– (1989)
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