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Cyclic presentations of the trivial group. (English) Zbl 1044.20016
Summary: We report on a computational group theory experiment involving a search for cyclic presentations of the trivial group. The list of such presentations obtained includes counterexamples to a conjecture of M. J. Dunwoody.

MSC:
20F05 Generators, relations, and presentations of groups
68W30 Symbolic computation and algebraic computation
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References:
[1] Baumslag G., ”On the Andrews–Curtis equivalence” (1999)
[2] Burns R. G., Bull. London Math. Soc. 25 (6) pp 513– (1993) · Zbl 0796.20022
[3] Cavicchioli A., ”On a conjecture of M. J. Dunwoody” (1999)
[4] Dunwoody M. J., Groups –Korea 1994 (Pusan, 1994) pp 47– (1995)
[5] Higman G., J. London Math. Soc. 26 pp 61– (1951) · Zbl 0042.02201
[6] Holt D. F., Groups and computation (New Brunswick, NJ, 1991) pp 113– (1993) · Zbl 0808.20008
[7] Johnson D. L., Topics in the theory of group presentations (1980) · Zbl 0437.20026
[8] Pride S. J., J. London Math. Soc. (2) 36 (2) pp 245– (1987) · Zbl 0633.20022
[9] Song H. J., ”Dunwoody 3-manifolds and (1, l)-decomposable knots” (1999)
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