Products of conjugacy classes and irreducible characters in finite camina groups

Liu, Yang; Yang, Shaohui

doi:10.22108/ijgt.2026.148288.2015

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	Products of conjugacy classes and irreducible characters in finite camina groups
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 24 تیر 1405 اصل مقاله (429.22 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2026.148288.2015
نویسندگان
Yang Liu^* ؛ Shaohui Yang
School of Mathematical Science, Tianjin Normal University, Tianjin 300387, P. R. China
چکیده
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.
کلیدواژه‌ها
Camina group؛ conjugacy class؛ character product

مراجع
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Products of conjugacy classes and irreducible characters in finite camina groups