Volume 36 • Number 3 • 2013   • On Lockett Pairs and Lockett Conjecture for $\pi$-Soluble Fitting Classes Lujin Zhu, Nanying Yang and N. T. Vorob'ev Abstract. In this paper, we construct a new and wide family of Lockett pairs in the class of all finite $\pi$-soluble groups and give a new characteristic of the validity of Lockett conjecture. As application, some known results are followed. 2010 Mathematics Subject Classification: 20D10 Full text: PDF