Some Equalities which Hold in the (n,m)-Group (Q,A) for $n\geq 2m$

Radoslav Galić, Anita Katić

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 $A(x_{1}^{m}, b_{1}^{n-2m}, y_{1}^{m}) = A\bigl(A(x_{1}^{m}, a_{1}^{n-2m}, (a_{1}^{n-2m}, e(b_{1}^{n-2m}))^{-1}), a_{1}^{n-2m}, y_{1}^{m}\bigr)$.