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Ultima descărcare din IBN: 2022-03-20 22:13 |
SM ISO690:2012 SHAH, Muhammad, ASIF, Ali, SORGE, Volker. Nuclei and commutants of C-loops. In: Quasigroups and Related Systems, 2013, vol. 21, nr. 1(29), pp. 97-102. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 21, Numărul 1(29) / 2013 / ISSN 1561-2848 | ||||||
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Pag. 97-102 | ||||||
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C-loops are loops that satisfy the identity x(y(yz)) = ((xy)y)z. In this note we use the order of nuclei of C-loops to show that (1) nonassociative C-loops of order 2p, where p is prime, are Steiner loops, (2) nonassociative C-loops of order 3n are non-simple and non-Steiner, (3) no nonassociative C-loop of order 2·3t, t > 1 exists, and (4) if every element of the commutant of a C-loop is of odd order the commutant forms a subloop. |
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Cuvinte-cheie C-loop, Steiner loop, commutant, nucleus |
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