Open Access
2016 Some Local Properties Defining ${\mathcal T}_0$-Groups and Related Classes of Groups
A. Ballester-Bolinches, J.C. Beidleman, R. Esteban-Romero, M.F. Ragland
Publ. Mat. 60(1): 265-272 (2016).


We call $G$ a $\operatorname{Hall}_{\mathcal X}$-group if there exists a normal nilpotent subgroup $N$ of $G$ for which $G/N'$ is an ${\mathcal X}$-group. We call $G$ a ${\mathcal T}_0$-group provided $G/\Phi(G)$ is a ${\mathcal T}$-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define $\operatorname{Hall}_{\mathcal X}$-groups and ${\mathcal T}_0$-groups where ${\mathcal X}\in\{ {\mathcal T},\mathcal {PT},\mathcal {PST}\}$; the classes $\mathcal {PT}$ and $\mathcal {PST}$ denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.


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A. Ballester-Bolinches. J.C. Beidleman. R. Esteban-Romero. M.F. Ragland. "Some Local Properties Defining ${\mathcal T}_0$-Groups and Related Classes of Groups." Publ. Mat. 60 (1) 265 - 272, 2016.


Published: 2016
First available in Project Euclid: 22 December 2015

zbMATH: 1342.20013
MathSciNet: MR3447741

Primary: 20D10 , 20D20 , 20D35

Keywords: $\mathcal{PST}$-group , $\mathcal{T}$-group , finite solvable group , Subnormal subgroup

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.60 • No. 1 • 2016
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