Geodesic
A survey article on some subgroup embeddings and local properties for soluble $\mathrm{PST}$-groups
Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 197-203

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Let $G$ be a group and $p$ a prime number. $G$ is said to be a $Y_p$-group if whenever $K$ is a $p$-subgroup of $G$ then every subgroup of $K$ is an $S$-permutable subgroup in $N_G(K)$. The group $G$ is a soluble $\mathrm{PST}$-group if and only if $G$ is a $Y_p$-group for all primes $p$. One of our purposes here is to define a number of local properties related to $Y_p$ which lead to several new characterizations of soluble $\mathrm{PST}$-groups. Another purpose is to define several embedding subgroup properties which yield some new classes of soluble $\mathrm{PST}$-groups. Such properties include weakly S-permutable subgroup, weakly semipermutable subgroup, and weakly seminormal subgroup.
Keywords: $\mathrm{S}$-permutable subgroup, semipermutable subgroup, seminormal subgroup, $\mathrm{PST}$-group. 
@article{ADM_2017_23_2_a1,
     author = {James. C. Beidleman},
     title = {A survey article on some subgroup embeddings and local properties for soluble $\mathrm{PST}$-groups},
     journal = {Algebra and discrete mathematics},
     pages = {197--203},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a1/}
}
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James. C. Beidleman. A survey article on some subgroup embeddings and local properties for soluble $\mathrm{PST}$-groups. Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 197-203. http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a1/