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Units of modular group algebrasLet RG denote the group ring of the group G over the ring R and U(RG) denote the unit group of RG. The objective of this thesis is to become familiar with the techniques used to establish U(RG) in a recently published article. We begin with an introduction to groups, rings and elds. Group rings are then discussed and in particular, the decomposition of RG. We conclude with the structure of U(F3kD6).