On single-law definitions of groups

It will be proved that any mononomic variety of groups can be considered as a variety of (ρ ε) or (ρ, τ) or (ν, ε)-algebras, or as a variety of n-groupoids—which satisfy a single law, where: xyρ = x.y−1 = xτ = x−1, xyν = x−1.y−1, ε is the identity, and for certain interpretations of the n-ary operation. The problem is discussed for Ω-groups, too.