2024/08/07 by Sumana Hatui, Hatui, Sumana, Gurleen Kaur +3
Mathematics · #16S35 #20C25 #20E99 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2408.03666
openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The twisted group ring isomorphism problem (TGRIP) is a variation of the classical group ring isomorphism problem. It asks whether the ring structure of the twisted group ring determines the group up to isomorphism. In this article, we study the TGRIP for direct product and central product of groups. We provide some criteria to answer the TGRIP for groups by answering the TGRIP for the associated quotients. As an application of these results, we provide several examples. Finally, we answer the TGRIP for extra-special p-groups, and for the groups of order p5, where p ≥ 5 is a prime, except a list of five groups.