Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-6,
author = {Wenai Yan and Baojun Li and Zhirang Zhang},
title = {Conditions for p-supersolubility and p-nilpotency of finite soluble groups},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {85-98},
zbl = {1329.20026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-6}
}
Wenai Yan; Baojun Li; Zhirang Zhang. Conditions for p-supersolubility and p-nilpotency of finite soluble groups. Colloquium Mathematicae, Tome 131 (2013) pp. 85-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-6/