On the Twisted Group Ring Isomorphism Problem for a class of groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910559071371264 |
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| author | Hatui, Sumana Kaur, Gurleen Sabnam, Sahanawaj |
| author_facet | Hatui, Sumana Kaur, Gurleen Sabnam, Sahanawaj |
| contents | 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 $p^5$, where $p \geq 5$ is a prime, except a list of five groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Twisted Group Ring Isomorphism Problem for a class of groups Hatui, Sumana Kaur, Gurleen Sabnam, Sahanawaj Group Theory Representation Theory 16S35, 20C25, 20E99 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 $p^5$, where $p \geq 5$ is a prime, except a list of five groups. |
| title | On the Twisted Group Ring Isomorphism Problem for a class of groups |
| topic | Group Theory Representation Theory 16S35, 20C25, 20E99 |
| url | https://arxiv.org/abs/2408.03666 |