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The Problem of Freeness for Euler Monoids and Möbius Groups

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= {(a,b,t) epsilon Z 3 : a 2 + b 2 = t n, n≥ 1, is free if and only if n is odd (Theorem 1). We extend the results of Lyndon and Ullman, and Beardon concerning the set of those rational numbers mu epsilon (-2,2) for which the matrix Möbius group G mu generated by A= and B = is not free (Theorems 2, 3, 4).

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Authors
  1. Aleksander Grytczuk
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  2. Marek Wójtowicz
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Grytczuk, A., Wójtowicz, M. The Problem of Freeness for Euler Monoids and Möbius Groups. SemiGroup Forum 61, 277–282 (2000). https://doi.org/10.1007/PL00006024

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  • DOI: https://doi.org/10.1007/PL00006024

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