Some local properties defining \(\mathcal T_0\)-groups and related classes of groups. (English) Zbl 1342.20013

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

Publ. Mat., Barc. 60, No. 1, 265-272 (2016).

A group \(G\) is called a Hall\(_{\mathcal X}\)-group if there exists a normal nilpotent subgroup \(N\) of \(G\) for which \(G/N'\) is an \(\mathcal X\)-group (so, according to the famous theorem of P. Hall, Hall\(_{\mathcal N}\)-groups are just the nilpotent groups if \(\mathcal N\) denotes the class of nilpotent groups). The authors consider new classes of groups appearing as Hall\(_{\mathcal X}\)-groups where the classes \(\mathcal X\) are generalizations of \(\mathcal T\)-groups and \(\mathcal{PST}\)-groups.

Reviewer: Hermann Heineken (Würzburg)

MSC:

20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20	Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D15	Finite nilpotent groups, \(p\)-groups
20D35	Subnormal subgroups of abstract finite groups
20D40	Products of subgroups of abstract finite groups

Keywords:

subnormal subgroups; \(\mathcal T\)-groups; \(\mathcal{PST}\)-groups; finite solvable groups; transitive normality; transitive permutability