2025/08/18 by Thu T. H. Quan, Quan, Thu T. H., Hung P. Tong‐Viet +1
Mathematics · Physics and Astronomy · #20C15 #20D25 #20E34 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Group Theory (math.GR) #Mathematical Inequalities and Applications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2508.13056
openalex publication_date 2025/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate certain generalizations of Camina pairs. Let H be a nontrivial proper subgroup of a finite group G. We first show that every nontrivial irreducible complex character of H induces homogeneously to G if and only if for every x∈ G∖ H, the element x is conjugate to xh for all h∈ H. Furthermore we prove that if xh is conjugate to either x or x-1 for all h∈ H and all x∈ G∖ H, then the normal closure N of H in G also satisfies the same condition, and N is nilpotent. Finally, we determine the structure of H under the assumption that for every element x∈ G∖ H of odd order, the coset xH consists entirely of elements of odd order.