Received February 3, 2023. Published online May 6, 2024.
Abstract: We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.
Keywords: non-metabelian groups; finite field; group algebra; unit group
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Affiliations: Navamanirajan Abhilash, Elumalai Nandakumar, Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Chengalpattu District, Kattankulathur - 603203, Tamil Nadu, India, e-mail: an1295@srmist.edu.in, {nanda1611@gmail.com}; Rajendra Kumar Sharma, Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi - 110016, India, e-mail: rksharmaiitd@gmail.com; Gaurav Mittal (corresponding author), Defence Research and Development Organization, Near Metcalfe House, New Delhi - 110054, India, e-mail: gaurav.mittaltwins@yahoo.com