Formal sums and power series over a group

Formal series over a group are studied as an algebraic system with componen twise composition and a partial operation of convolution '*'. For right-ord ered groups a module of formal power series is introduced and studied; thes e are formal sums with well-ordered supports. Special attention is paid to systems of formal power series (whose supports are well-ordered with respec t to the ascending order) that form an L-basis, that is, such that every fo rmal power series can be expanded uniquely in this system. L-bases are rela ted to automorphisms of the module of formal series that have natural prope rties of monotonicity and a-linearity. The relations gamma * beta = 0 and g amma * beta = 1 are also studied. Note that in the case of a totally ordere d group the system of formal power series forms a skew field with valuation (Mal'tsev and Neumann, 1948-1949.). Bibliography: 6 titles.