The influence of p-regular class sizes on normal subgroups

The final publication is available at www.degruyter.comLet G be a finite group and N be a normal subgroup of G and suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. It is shown that N is solvable and that if H is a p-complement of N, then either H is abelian or H is the product of an r-group for some prime r not equal p and a central subgroup of G.The research of the second and third named authors was partially supported by the Spanish Government, Proyecto MTM2010-19938-C03-02 and by the Valencian Government, Proyecto PROM-ETEO/2011/30. The second named author was also supported by grant Fundacio Caixa-Castello P11B2010-47.Akhlaghi, Z.; Beltran, A.; Felipe Román, MJ. (2013). The influence of p-regular class sizes on normal subgroups. Journal of Group Theory. 16(4):585-593. https://doi.org/10.1515/jgt-2013-000258559316