Groupoids of order three up to isomorphisms

Chernov Vladimir; Demidova Valentina; Malyutina Nadezhda; Shcherbacov Victor

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2023-07-09 17:05

SM ISO690:2012

CHERNOV, Vladimir, DEMIDOVA, Valentina, MALYUTINA, Nadezhda, SHCHERBACOV, Victor. Groupoids of order three up to isomorphisms. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 141-143. ISBN 978-9975-81-074-6.

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Conference on Applied and Industrial Mathematics
Ediţia a 29, 2022

Conferința "Conference on Applied and Industrial Mathematics"
29, Chişinău, Moldova, 25-27 august 2022

Groupoids of order three up to isomorphisms

Pag. 141-143

Chernov Vladimir, Demidova Valentina, Malyutina Nadezhda, Shcherbacov Victor

Vladimir Andrunachievici Institute of Mathematics and Computer Science

Disponibil în IBN: 21 decembrie 2022

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List of all classical Bol-Moufang identities is given in [1]. We continue count of number non-isomorphic groupoids of order three with some Bol-Moufang identities [2, 3, 4, 5].There exist 26 non-isomorphic groupoids of order 3 with identity F9, (x.yz)x= x(yz.x) from possible 221 groupoids. There exist 159 non-isomorphic groupoids of order 3 with identity F10, x(y. zx) = x(yz.x) from possible 874 groupoids. Identity F11 xy.xz = (xy,x)z: up to isomorphism there exist 49 groupoids. Identity F12 xy.xz = (x.yx)z: up to isomorphism there exist 45 groupoids. Identity F13 xy.xz = x(yx.z): up to isomorphism there exist 53 groupoids. Identity F13 xy.xz = x(yx.z): up to isomorphism there exist 53 groupoids. Identity F14 xy.xz = x(y.xz): up to isomorphism there exist 61 groupoids. Identity F15 (xy.x)z = (x.yx)z: up to isomorphism there exist 253 groupoids. Identity F16 (xy.x)z = x(yx.z): up to isomorphism there exist 73 groupoids. Identity F17 (xy.x)z = x(yx.z): up to isomorphism there exist 35 groupoids. Identity F18 (x.yx)z = x(yx.z): up to isomorphism there exist 61 groupoids. Identity F19 (x.yx)z = x(y.xz): up to isomorphism there exist 40 groupoids. Identity F20 x(yx.z) = x(y.xz): up to isomorphism there exist 110 groupoids from possible 601.

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