Structure of the unit group of the group algebras of non-metabelian groups of order 128
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 de...
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| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2025-04-01
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| Series: | Mathematica Bohemica |
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| Online Access: | https://mb.math.cas.cz/full/150/1/mb150_1_1.pdf |
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| author | Navamanirajan Abhilash Elumalai Nandakumar Rajendra Kumar Sharma Gaurav Mittal |
| author_facet | Navamanirajan Abhilash Elumalai Nandakumar Rajendra Kumar Sharma Gaurav Mittal |
| author_sort | Navamanirajan Abhilash |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-58d046f350ed479ca7df5795169ec2db |
| institution | DOAJ |
| issn | 0862-7959 2464-7136 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj-art-58d046f350ed479ca7df5795169ec2db2025-08-20T03:00:54ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362025-04-01150112310.21136/MB.2024.0017-23MB.2024.0017-23Structure of the unit group of the group algebras of non-metabelian groups of order 128Navamanirajan AbhilashElumalai NandakumarRajendra Kumar SharmaGaurav MittalWe 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.https://mb.math.cas.cz/full/150/1/mb150_1_1.pdf non-metabelian groups finite field group algebra unit group |
| spellingShingle | Navamanirajan Abhilash Elumalai Nandakumar Rajendra Kumar Sharma Gaurav Mittal Structure of the unit group of the group algebras of non-metabelian groups of order 128 Mathematica Bohemica non-metabelian groups finite field group algebra unit group |
| title | Structure of the unit group of the group algebras of non-metabelian groups of order 128 |
| title_full | Structure of the unit group of the group algebras of non-metabelian groups of order 128 |
| title_fullStr | Structure of the unit group of the group algebras of non-metabelian groups of order 128 |
| title_full_unstemmed | Structure of the unit group of the group algebras of non-metabelian groups of order 128 |
| title_short | Structure of the unit group of the group algebras of non-metabelian groups of order 128 |
| title_sort | structure of the unit group of the group algebras of non metabelian groups of order 128 |
| topic | non-metabelian groups finite field group algebra unit group |
| url | https://mb.math.cas.cz/full/150/1/mb150_1_1.pdf |
| work_keys_str_mv | AT navamanirajanabhilash structureoftheunitgroupofthegroupalgebrasofnonmetabeliangroupsoforder128 AT elumalainandakumar structureoftheunitgroupofthegroupalgebrasofnonmetabeliangroupsoforder128 AT rajendrakumarsharma structureoftheunitgroupofthegroupalgebrasofnonmetabeliangroupsoforder128 AT gauravmittal structureoftheunitgroupofthegroupalgebrasofnonmetabeliangroupsoforder128 |