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Articolul precedent |
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706 5 |
Ultima descărcare din IBN: 2023-05-26 13:09 |
Căutarea după subiecte similare conform CZU |
512.542.55+512.548 (1) |
Алгебра (410) |
SM ISO690:2012 FOGUEL, Tuval, HILLER, Josh. On Bruck's prolongation and contraction maps. In: Quasigroups and Related Systems, 2019, vol. 27, nr. 1(41), pp. 53-62. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 27, Numărul 1(41) / 2019 / ISSN 1561-2848 | ||||||
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CZU: 512.542.55+512.548 | ||||||
MSC 2010: 20N05. | ||||||
Pag. 53-62 | ||||||
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Rezumat | ||||||
Bruck constructed the rst prolongation and contraction of quasigroups in order to study Steiner triple systems. In this paper we dene a new family of quasigroups: The SteinerBruck quasigroups (SB-quasigroups), where aa2 = a2a and a2 = b2 for all possible a and b, which arise from Bruck's prolongation. We use Bruck's prolongation and contraction maps to explore properties of this family of quasigroups. Among other results, we show that there is a one-to-one correspondence between SB-quasigroups and uniquely 2-divisible quasigroups. As a corollary to this result we nd a correspondence between idempotent quasigroups and loops of exponent 2. We then use this correspondence to study some interesting loops of exponent two and some interesting idempotent quasigroups. |
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Cuvinte-cheie Finite groups of exponent 2, nite loops of exponent 2, nite idempotent quasigroups, polongation of, Latin square, contraction of, Latin square |
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