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 SM ISO690:2012DUDEK, Wieslaw, MONZO, Robert. Translatable isotopes of finite groups. In: Quasigroups and Related Systems, 2021, vol. 29, nr. 2(46), pp. 193-208. ISSN 1561-2848. |
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 Quasigroups and Related Systems |
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| Volumul 29, Numărul 2(46) / 2021 / ISSN 1561-2848 | ||||||
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| Pag. 193-208 | ||||||
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We prove the main result, that if (Q; ) is a k-translatable isotope of a finite group (Q;) of order n then (Q;) is isomorphic to the additive group Zn of integers modulo n. Given a k-translatable ordering of a left cancellative groupoid Q of order n, we determine all k-translatable orderings of Q. We also prove that a left-cancellative, k-translatable groupoid Q is translatable for a single value of k. Finally, we prove that a left (or right) linear isotope of Zn is linear and we give examples of k-translatable isotopes of Z4 that are neither left nor right linear. |
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