The structure of the unit group of the group algebra F _2kD ₈

Let RG denote the group ring of the group G over the ring R. Using an isomorphismbetween RG and a certain ring of n×n matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order 8 over any finite field of chracteristic 2 is determined in terms of split extensions of cyclic groups.