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Structural taxonomy and complex irreducible representations of non-abelian groups of order p^4
Abstract
Let p be an odd prime and let G be a non-abelian group of order p4. The classification of groups of order p4 provides a natural setting for studying the structure of their complex group algebras. In this paper, we consider a non-abelian group G of order p4 and determine the primitive central idempotents of the complex group algebra ℂG. Using these idempotents, we obtain the corresponding decomposition of ℂG into simple components and describe the irreducible representations of G. The results provide an explicit description of the representation-theoretic structure of the chosen non-abelian group of order p4 and illustrate the role of primitive central idempotents in the Wedderburn decomposition of its complex group algebra.
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BibTeX
@misc{shukla2026structural,
title = {{Structural taxonomy and complex irreducible representations of non-abelian groups of order p^4}},
author = {Satyam Shukla and Jagmohan Tanti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35198},
eprint = {2610.35198},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35198},
}
RIS
TY - UNPB
TI - Structural taxonomy and complex irreducible representations of non-abelian groups of order p^4
AU - Satyam Shukla
AU - Jagmohan Tanti
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35198
UR - https://arxiv.org/abs/2610.35198
AB - Let p be an odd prime and let G be a non-abelian group of order p^4. The classification of groups of order p^4 provides a natural setting for studying the structure of their complex group algebras. In this paper, we consider a non-abelian group G of order p^4 and determine the primitive central idempotents of the complex group algebra ℂG. Using these idempotents, we obtain the corresponding decomposition of ℂG into simple components and describe the irreducible representations of G. The results provide an explicit description of the representation-theoretic structure of the chosen non-abelian group of order p^4 and illustrate the role of primitive central idempotents in the Wedderburn decomposition of its complex group algebra.
ER -