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<creators>
<creator>
<creatorName>Dudek, W.A.</creatorName>
<affiliation>Wroclaw University of Science and Technology, Polonia</affiliation>
</creator>
<creator>
<creatorName>Monzo, R.A.</creatorName>
<affiliation>Necunoscută, Marea Britanie, Marea Britanie</affiliation>
</creator>
</creators>
<titles>
<title xml:lang='en'>Translatable isotopes of finite groups</title>
</titles>
<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2021</publicationYear>
<relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>1561-2848</relatedIdentifier>
<dates>
<date dateType='Issued'>2021-12-28</date>
</dates>
<resourceType resourceTypeGeneral='Text'>Journal article</resourceType>
<descriptions>
<description xml:lang='en' descriptionType='Abstract'><p>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.</p></description>
</descriptions>
<formats>
<format>application/pdf</format>
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