Invertibility criterion of composition of two multiary quasigroups

Abstract

We study the Invertibility of operations that are a composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T-quasigroups. For this purpose, we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [G. Belyavskaya, G. Mullen, Orthogonal hypercubes and n-ary operations, Quasigroups Related System 13 (2005), no. 1, 73-86]/ we establish some relations between these notions and give illustrative examples/