New conditions on maximal invariant subgroups that imply solubility
A Beltrán, C Shao - Results in Mathematics, 2023 - Springer
Let G be a finite group and assume that a finite group of automorphisms A acts on G, such
that the orders of A and G are relatively prime. We prove that the fact of imposing certain …
that the orders of A and G are relatively prime. We prove that the fact of imposing certain …
A new criterion for p-nilpotency and solvability of finite groups by coprime actions
B Zhang, J Lu, W Meng - Communications in Algebra, 2024 - Taylor & Francis
Let G and A be finite groups of relative coprime orders and A acts on G via automorphisms.
In this paper, we investigate the p-nilpotency and solvability of finite groups in which every …
In this paper, we investigate the p-nilpotency and solvability of finite groups in which every …
Finite groups whose maximal subgroups are 2-nilpotent or normal
C Shao, A Beltrán - Bulletin of the Malaysian Mathematical Sciences …, 2024 - Springer
We describe the structure of those finite groups whose maximal subgroups are either 2-
nilpotent or normal. Among other properties, we prove that if such a group G does not have …
nilpotent or normal. Among other properties, we prove that if such a group G does not have …
c-Normality and coprime action in finite groups
A Beltrán, C Shao - Acta Mathematica Hungarica, 2023 - Springer
A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G
such that G= HN and H∩ N≤ core G (H), the largest normal subgroup of G contained in H. c …
such that G= HN and H∩ N≤ core G (H), the largest normal subgroup of G contained in H. c …
[引用][C] Sylowizers and p-nilpotency in finite groups
B Zhang, J Lu, W Meng - Journal of Algebra and its Applications, 2024 - World Scientific
Let G and A be finite groups of relative coprime orders and A act on G via automorphisms.
An A-invariant subgroup S of G is called an Ap-Sylowizer of an A-invariant p-subgroup R if S …
An A-invariant subgroup S of G is called an Ap-Sylowizer of an A-invariant p-subgroup R if S …