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Title: The infinite dihedral group and some properties of it's group algebra

Abstract: Group algebras are easily defined rings whose properties we might study. We will start with some general results and illuminating examples. Then we will focus on rings that are CS or PP (these will be defined). An example of particular interest is the group algebra of the infinite dihedral group which has both of the properties as long as the characterisitic of the field is not 2. What other group rings share these?

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