@article{Algreagri2026, 
author = {Manal H. Algreagri},
title = {On eigenvalues of the Cartan matrices for    p-constrained groups},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {19046-19057},
keywords = {finite group, p-constrained groups, block, defect group, eigenvalues, nonnegative matrices},
url = {https://www.sciopen.com/article/10.3934/math.2026776},
doi = {10.3934/math.2026776},
abstract = {Let    p be a prime number. For    p-constrained groups, we demonstrated that the Perron–Frobenius eigenvalue of the Cartan matrix of a    p-block    B was bounded above by the order of its defect group. The proof employed block-theoretic methods, spectral bounds in modular representation theory, and structural        p    ′  -reduction techniques. This conclusion extended a previously established inequality for    p-solvable groups to the larger class of    p-constrained groups. Finally, we presented computational results regarding the relationship between elementary divisors and eigenvalues of Cartan matrices for    p-constrained groups that were not    p-solvable.}
}