Finite p-supersoluble groups with some E-S-supplemented subgroups CHANGWEN LI (*) -XIAOLONG YU (**) -NA TANG ( z )ABSTRACT -Let H be a subgroup of a group G and H eG denote the subgroup of H generated by all those subgroups of H which are S-permutably embedded in G.H is said to be E-S-supplemented in G if there exists a subnormal subgroup T of G such that G HT and H T H eG . In this paper, we investigate the influence of some E-S-supplemented subgroups on the structure of finite groups. Some new characterizations of p-supersoluble groups are obtained.MATHEMATICS SUBJECT CLASSIFICATION (2010). 20D10, 20D20.
We prove that a finite group G is p-supersolvable or p-nilpotent if some subgroups of G are weakly s-semipermutable in G. Several earlier results are generalized.
Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be $E$-supplemented in $G$ if there is a subgroup $T$ of $G$ such that $G= HT$ and $H\cap T\leq {H}_{eG} $, where ${H}_{eG} $ denotes the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-quasinormally embedded in $G$. In this paper, some new characterisations of $p$-supersolubility of finite groups are given under the assumption that some primary subgroups are $E$-supplemented.
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