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January 25, 2026The Ramanujan Journal0 citationsOpen Access

Arithmetic properties of character degrees and the generalised knutson index

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DDDiego Martín Duro

Key Points

  • This research aims to introduce the generalized Knutson Index and analyze its properties related to character degrees.
  • Introduced the generalized Knutson Index.
  • Computed for special linear groups and projective special linear groups of degree two.
  • Classified alternating and symmetric groups based on the lowest common multiple of their irreducible representation degrees.
  • Determined the generalized Knutson Index for specific groups.
  • Classified groups where the lowest common multiple of degrees equals the group order.
  • Established a lower bound for the generalized Knutson Indices of alternating and symmetric groups.

Abstract

Abstract In this paper, we introduce the generalised Knutson Index and compute it for the special linear groups and projective special linear groups of degree two by computing the lowest common multiple of the degrees of their irreducible representations. We also classify all alternating and symmetric groups such that the lowest common multiple of the degrees of their irreducible representations equals the order groups, which yields a lower bound on the generalised Knutson Indices of these groups.

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Cite This Study

Diego Martín Duro (2026) studied this question.

synapsesocial.com/papers/6975b4fd5a65d392b01e5be6https://doi.org/10.1007/s11139-025-01311-3
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