id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5993	Allehyani, A. S.	Finite Groups with Certain $\mathcal{SSH}$-subgroups	2025	13	.pdf	application/pdf	6995	408	81	Clearly, P1 ⊴ G and (G/P1)/(H/P1) ∼=265 G/H ∈ F. By using similar arguments as in the second paragraph of (1) in Theorem 2,266 we can see that G/P1 ∈ F. But P1 ⩽ Φ(G), then G/Φ(G) ∈ F and, since F is saturated,267 we have G ∈ F, a contradiction. Let H and L be normal subgroups of G and let p ∈ π(G).	cache/ejpam-5993.pdf	txt/ejpam-5993.txt