پديدآورندگان :
Akhlaghi Zeinab z-akhlaghi@aut.ac.ir Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran , Beltrán Antonio abeltran@mat.uji.es Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain , José Felipe María mfelipe@mat.upv.es Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain , Khatami Maryam m.khatami@sci.ui.ac.ir Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran
كليدواژه :
Finite groups , Conjugacy class sizes , p , regular elements.
چكيده فارسي :
Let p be a prime and G be a finite p-solvable group. First we prove that if the set of conjugacy
class sizes of p-regular elements of G is {1; p^a; p^a m}, or {1;m; p^a m} where (m; p) = 1, then
m = q^b, for some prime q and the structure of p-complements of G is determined. Th en we show
that if N is a normal subgroup of finite p-solvable group G, and the p-regular elements of N have
exactly two G-conjugacy class sizes, then the p-complements of N are nilpotent.
