October 9, 2025Open Access

Minimal-order groups with an irreducible character of degree p or p²

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Finite groups of minimal order are classified based on the presence of irreducible characters of degree p or p^2.
The research identifies prime number conditions affecting group structure and character degrees.
A focus on representations illuminates the significance of irreducible characters in abstract algebra.
Understanding these groups enriches the study of complex characters and their applications within group theory.

Implication

The study characterizes finite groups with minimal order that have irreducible characters of degree p or p^2, highlighting implications for group theory.

Abstract

We characterize the finite groups of minimal order that admit an irreducible complex character of degree p or p², where p is a prime.

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Andrés Arranz (2025) studied this question.

synapsesocial.com/papers/68e7f0af2d7e30942762c7e7 https://doi.org/10.48550/arxiv.2507.19571

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Implication

The study characterizes finite groups with minimal order that have irreducible characters of degree p or p^2, highlighting implications for group theory.

Abstract

We characterize the finite groups of minimal order that admit an irreducible complex character of degree p or p², where p is a prime.

Minimal-order groups with an irreducible character of degree p or p²

Key Points

Implication

Abstract

Discussion

Cite This Study

Minimal-order groups with an irreducible character of degree p or p²

Key Points

Implication

Abstract

Discussion

Cite This Study

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