Unit group of semisimple group algebra of groups of order 36

Upadhyay, Diksha and Chandra, Harish (2025) Unit group of semisimple group algebra of groups of order 36. Annales Mathematicae et Informaticae, 62. pp. 143-155. ISSN 1787-5021 (Print) 1787-6117 (Online)

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Abstract

In this paper, we classify the structure of the unit group of semisimple group algebras over groups of order 36. There are 14 noniso morphic groups of this order, 10 of which are nonabelian. The structures of the unit groups of the group algebras corresponding to all abelian groups of order 36, as well as the groups C3 ×A4 and D36, have already been studied. This work focuses on the remaining 8 non-abelian groups of order 36, provid ing a detailed examination of the unit group structures of their corresponding semisimple group algebras.

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