Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
On matrix representations of groups of order 푝5 over ℚ. |
| 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: |
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