Some characterizations of finite \(\sigma\)-soluble \(P\sigma T\)-groups (Q1682069)

The paper is a continuing work of some early papers [the author, J. Algebra 436, 1--16 (2015; Zbl 1316.20020); J. Algebra Appl. 15, No. 5, Article ID 1650085, 13 p. (2016; Zbl 1348.20021); Commun. Math. Stat. 4, No. 3, 281--309 (2016; Zbl 1394.20011)]. Here, the author introduces a new concept of a \(P\sigma T\)-group. A \(P\sigma T\)-group is a group in which \(\sigma\)-permutability is a transitive relation in \(G\). Since \(\sigma\)-permutability is \(S\)-permutability for \(\sigma = \{\{2\}, \{3\}, \cdots,\}\), a \(P\sigma T\)-group is a generalization of \(PST\)-group. The author obtains some characterizations of finite \(\sigma\)-soluble \(P\sigma T\)-group.