A new model of the free monogenic digroup

It is well-known that one of open problems in the theory Leibniz algebras to find asuitable generalization Lie’s third theorem which associates a (local) Lie group any Liealgebra, real or complex. turns out, this related finding an appropriate analogue Liegroup for algebras. Using notion digroup, Kinyon obtained partial solution ofthis problem, namely, class so-called split Leibnizalgebras. A digroup nonempty set equipped with two binary associative operations, aunary operation and nullary satisfying additional axioms relating these operations.Digroups generalize groups have close relationships dimonoids dialgebras,the trioids trialgebras, other structures. Recently, G. Zhang Y. Chen applied themethod Grobner–Shirshov bases dialgebras construct free arbitraryrank, particular, they considered monogenic case separately. In paper, we give simplerand more convenient model digroup. We new classof digroups are based on commutative show how groupcan be from by suitable factorization.