let G be a C -infinity manifold and there exist a c-infinity n-ary operation f from G cartesian G....G to G defined by f(x_1,x_2,....,x_n)=x_1x_2....x_n and generalized inverse is C -infinity

in this case G is called a lie n-ary groups or lie -multiary group or

lie lie -polyadic group.

updated by @dariushaghababayeedehkordi: 21/01/17 10:16:28PM