Products of conjugacy classes and irreducible characters in finite camina groups

Articles in Press

Document Type : Research Paper

Authors

School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China

10.22108/ijgt.2026.148288.2015

Abstract

This paper investigates two problems concerning products of conjugacy classes and irreducible characters in finite groups. First, we provide a simplified proof of Dade and Yadav's theorem concerning groups in which the conjugacy class product $x^Gy^G=(xy)^G$ holds for all $x\in G, y\in G-(x^{-1})^G$. By using the classification of Camina groups due to Dark and Scoppola, we demonstrate that such groups are either abelian, non-abelian Camina $p$-groups, or specific Frobenius groups of the form $F^{+}\rtimes F^{\times}$ for some finite field $F$ with $|F|>2$ or $E_9\rtimes Q_8$. Second, we explore the dual problem for characters: groups in which the product of any two non-conjugate irreducible characters has exactly one irreducible constituent. We establish that such groups are precisely the Camina $p$-groups and the two families of Frobenius groups mentioned above.

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References

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International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 15 July 2026

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  • Receive Date: 07 February 2026
  • Revise Date: 23 June 2026
  • Accept Date: 03 July 2026
  • Published Online: 15 July 2026

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