Academic Journal
On matrix representations of groups of order 푝5 over ℚ.
| Τίτλος: | On matrix representations of groups of order 푝5 over ℚ. |
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| Συγγραφείς: | Choudhary, Ram Karan1 (AUTHOR) ramkchoudhary1997@gmail.com, Prajapati, Sunil Kumar1 (AUTHOR) skprajapati@iitbbs.ac.in |
| Πηγή: | Journal of Group Theory. Sep2026, Vol. 29 Issue 5, p1007-1044. 38p. |
| Θεματικοί όροι: | *Representations of groups (Algebra), *Representation theory, *Group algebras |
| Περίληψη: | In this article, we study rational representations of groups of order p 5 , where 푝 is an odd prime. For a 푝-group 퐺 and an irreducible complex character 휒 of 퐺, the construction of an irreducible rational matrix representation of 퐺 affording the character Ω (χ) is equivalent to determining a pair (H , ψ) , with 퐻 a subgroup of 퐺 and 휓 a linear character of 퐻 such that ψ G = χ and Q (ψ) = Q (χ) , where Ω (χ) = m Q (χ) ∑ σ ∈ Gal (Q (χ) / Q) χ σ and m Q (χ) denotes the Schur index of 휒 over ℚ. For each inequivalent irreducible rational representation of every group of order p 5 , we determine such a pair, referred to as a required pair. We also derive combinatorial formulations for the Wedderburn decomposition of rational group algebras of these 푝-groups, using results from their rational representations. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: asx DbLabel: Academic Search Index An: 196670807 RelevancyScore: 1452 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1452.42749023438 |
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| Items | – Name: Title Label: Title Group: Ti Data: On matrix representations of groups of order 푝<superscript>5</superscript> over ℚ. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Choudhary%2C+Ram+Karan%22">Choudhary, Ram Karan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ramkchoudhary1997@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Prajapati%2C+Sunil+Kumar%22">Prajapati, Sunil Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> skprajapati@iitbbs.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Group+Theory%22">Journal of Group Theory</searchLink>. Sep2026, Vol. 29 Issue 5, p1007-1044. 38p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Representations+of+groups+%28Algebra%29%22">Representations of groups (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Group+algebras%22">Group algebras</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this article, we study rational representations of groups of order p 5 , where 푝 is an odd prime. For a 푝-group 퐺 and an irreducible complex character 휒 of 퐺, the construction of an irreducible rational matrix representation of 퐺 affording the character Ω (χ) is equivalent to determining a pair (H , ψ) , with 퐻 a subgroup of 퐺 and 휓 a linear character of 퐻 such that ψ G = χ and Q (ψ) = Q (χ) , where Ω (χ) = m Q (χ) ∑ σ ∈ Gal (Q (χ) / Q) χ σ and m Q (χ) denotes the Schur index of 휒 over ℚ. For each inequivalent irreducible rational representation of every group of order p 5 , we determine such a pair, referred to as a required pair. We also derive combinatorial formulations for the Wedderburn decomposition of rational group algebras of these 푝-groups, using results from their rational representations. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196670807 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1515/jgth-2025-0120 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 1007 Subjects: – SubjectFull: Representations of groups (Algebra) Type: general – SubjectFull: Representation theory Type: general – SubjectFull: Group algebras Type: general Titles: – TitleFull: On matrix representations of groups of order 푝5 over ℚ. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Choudhary, Ram Karan – PersonEntity: Name: NameFull: Prajapati, Sunil Kumar IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 14335883 Numbering: – Type: volume Value: 29 – Type: issue Value: 5 Titles: – TitleFull: Journal of Group Theory Type: main |
| ResultId | 1 |