Paper “Some Local Properties Defining T₀-Groups and Related Classes of Groups” published in Publ. Mat.

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A. Ballester-Bolinches, J. C. Beidleman, R. Esteban-Romero, and M. F. Ragland

Some local properties defining T0-groups and related classes of groups

Publ. Mat., 60(1):265–272, 2016


We call G a Hall_χ-group if there exists a normal nilpotent subgroup N of G for which G/N is an χ-group. We call G a T-group provided G/Φ(G) is a T-group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define Hall_χ-groups and T-groups where χ{T, PT, PST}; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations.

2010 Mathematical Subject Classification: 20D10, 20D20, 20D35

Keywords: Subnormal subgroup, T-group, PST-group, finite solvable group