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Summands of finite group algebras

Carsten DietzelGaurav Mittal — 2021

Czechoslovak Mathematical Journal

We study the inverse problem of the determination of a group algebra from the knowledge of its Wedderburn decomposition. We show that a certain class of matrix rings always occur as summands of finite group algebras.

On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav MittalRajendra Kumar Sharma — 2021

Mathematica Bohemica

We characterize the unit group of semisimple group algebras 𝔽 q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ( ( C 3 × C 3 ) C 3 ) C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

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