WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Finite Group with c-Normal or s-Quasinormally Embedded Subgroups
Author:
Abstract: If P is a p-group for some prime $$p$$ we shall write $$M(P)$$ to denote the set of all maximal subgroups of $$P$$ and $$M_{d}(P) = \left \{ P_{1}, ..., P_{d}
\right \}$$ to denote any set of maximal subgroups of $$P$$ such that $$\bigcap_{i=1}^{d} P_{i} = Φ(P)$$ and $$d$$ is as small as possible. In this paper, the structure of a finite group $$G$$ under some assumptions on the c-normal or s-quasinormally embedded subgroups in $$M_{d}(P)$$, or each prime $$p$$, , and Sylow p-subgroups $$P$$ of $$G$$ is researched. Some known results are generalized.