We investigate the structure of finite groups whose noncentral real class sizes have the same -part. In particular, we prove that such groups are solvable and have -length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.
"2-parts of real class sizes." Algebra Number Theory 12 (10) 2499 - 2514, 2018. https://doi.org/10.2140/ant.2018.12.2499