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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Main Authors: Navamanirajan Abhilash, Elumalai Nandakumar, Rajendra Kumar Sharma, Gaurav Mittal
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2025-04-01
Series:Mathematica Bohemica
Subjects:
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
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institution DOAJ
issn 0862-7959
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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