Journal of Prime Research in Mathematics

On some characterization of nearly Hall S-semiembedded subgroups of finite groups

Iftikhar Ali\(^a\), Abid Mahboob\(^{b,*}\), Taswer Hussaain\(^c\), Faryal Chaudhry\(^a\)
\(^a\)Department of Mathematics and Statistics, The University of Lahore, Pakistan.
\(^b\)Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan.
\(^c\)Department of Mathematics, Punjab Education Department, Lahore, Pakistan.
Correspondence should be addressed to: Abid Mahboob at abid.mahboob@ue.edu.pk

Abstract

Let K be a subgroup. Then K is known as partially Hall s-semiembedded subgruop in \(\Game\) if for K\(\mathcal{T}\) is s-semi permutable in \(\Game\) and K \(\cap \mathcal{T} \leq\) \(K_{\tilde{s} \Game}\) where \(K _{\tilde{s} \Game}\) generated by all those subgroups of K which are Hall s-semiembedded in \(\Game\), there exists a normal subgroup \(\mathcal{T}\) of G. In this paper, we investigate the notion of partially Hall \(S\)-semi embedded subgroups on the structure of finite group \(\Game\). We obtain some new criteria related to the \(p\)-nilpotency and super solubility of a finite group. Some earlier results about formations are also generalized by our results.

Keywords:

Hall s-semiembedded subgroups, Partially \(S\)-embeded subgroup, \(p\)-nilpotent.