Some Equalities which Hold in the (n,m)-Group (Q,A) for $n\geq 2m$
Mathematica Moravica, Tome 14 (2010) no. 1.
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In this paper, we have proved two equalities which hold in an $(n,m)$-group $(Q,A)$ for $n\geq 2m$. The first of them is a generalization of the equality $(a\cdot b)^{-1} = b^{-1}\cdot a^{-1}$, which holds in the binary group $(Q,\cdot)$. The second of them is equality $A(x_{1}^{m}, b_{1}^{n-2m}, y_{1}^{m}) = A\bigl(A(x_{1}^{m}, a_{1}^{n-2m}, (a_{1}^{n-2m}, e(b_{1}^{n-2m}))^{-1}), a_{1}^{n-2m}, y_{1}^{m}\bigr)$.
Mots-clés :
(n;m)-group, {1, n − m + 1}-neutral operation, inverse operation of the (n;m)-groupoid
@article{MM3_2010_14_1_a4, author = {Radoslav Gali\'c and Anita Kati\'c}, title = {Some {Equalities} which {Hold} in the {(n,m)-Group} {(Q,A)} for $n\geq 2m$}, journal = {Mathematica Moravica}, pages = {47 - 51}, publisher = {mathdoc}, volume = {14}, number = {1}, year = {2010}, url = {https://geodesic-test.mathdoc.fr/item/MM3_2010_14_1_a4/} }
Radoslav Galić; Anita Katić. Some Equalities which Hold in the (n,m)-Group (Q,A) for $n\geq 2m$. Mathematica Moravica, Tome 14 (2010) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2010_14_1_a4/