2017
Том 69
№ 9

All Issues

Second Maximal Subgroups of a Sylow p-Subgroup and the p-Nilpotency of Finite Groups

Li X. H., Xu Y.


Abstract

A subgroup H of a group G is said to be weakly s-semipermutable in G if G has a subnormal subgroup T such that HT = G and HT ≤ \( {H}_{\overline{s}G} \) , where \( {H}_{\overline{s}G} \) is the subgroup of H generated by all subgroups of H that are s-semipermutable in G. The main aim of the paper is to study the p-nilpotency of a group for which every second maximal subgroup of its Sylow p-subgroups is weakly s-semipermutable. Some new results are obtained.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 5, pp 775-780.

Citation Example: Li X. H., Xu Y. Second Maximal Subgroups of a Sylow p-Subgroup and the p-Nilpotency of Finite Groups // Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 694–698.