Jiangtao Shi

collaborators

5 papers

math.GR2025

On an extension of Shlyk's theorem

Jiangtao Shi, Fanjie Xu, Na Li

In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which pr…

math.GR2025

Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent

Jiangtao Shi, Mengjiao Shan, Fanjie Xu

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. For any fixed prime divisor $p$ of $∣ G ∣$ , we provide a complete characterization of the struc…

math.GR2025

Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power

Jiangtao Shi, Mengjiao Shan, Fanjie Xu

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, assume that $G$ has a maximal $A$ -invariant subgroup $M$ that is a direct product of some iso…

math.GR2024

Finite groups with some particular maximal invariant subgroups being nilpotent or all non-nilpotent maximal invariant subgroups being normal

Jiangtao Shi, Fanjie Xu

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. We provide a complete classification of a finite group $G$ in which every maximal $A$ -invaria…

math.GR2024

On generalizations of Iwasawa's theorem

Jiangtao Shi, Fanjie Xu, Mengjiao Shan

Iwasawa's theorem indicates that a finite group $G$ is supersolvable if and only if all maximal chains of the identity in $G$ have the same length. As generalizations of Iwasawa's…

On an extension of Shlyk's theorem

Finite groups in which every maximal invariant subgroup of order divisible by p is nilpotent

Finite groups in which some particular non-nilpotent maximal invariant subgroups have indices a prime-power

Finite groups with some particular maximal invariant subgroups being nilpotent or all non-nilpotent maximal invariant subgroups being normal

On generalizations of Iwasawa's theorem

Finite groups in which every maximal invariant subgroup of order divisible by $p$ is nilpotent