On unit groups of modular group algebras

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The analysis focuses on unit groups of group algebras KG for non-abelian p-groups G and fields K with characteristic p. By examining the core and normalizer of U within the normalized units of 1 + rad(KG), the authors extend previous findings by K.R. Pearson and D.B. Coleman. This is achieved through the application of fixed points from enhanced group actions, offering new insights into the structure and properties of these mathematical entities.