2019
Том 71
№ 9

All Issues

Li X. H.

Articles: 2
Brief Communications (English)

$s$-Conditionally Permutable Subgroups and $p$-Nilpotency of Finite Groups

Li X. H., Xu Y.

↓ Abstract

Ukr. Mat. Zh. - 2014. - 66, № 6. - pp. 858–864

We study the $p$-nilpotency of a group such that every maximal subgroup of its Sylow $p$-subgroups is $s$-conditionally permutable for some prime $p$. By using the classification of finite simple groups, we get interesting new results and generalize some earlier results.

Article (English)

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

Li X. H., Xu Y.

↓ Abstract

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 694–698

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.