On generalised FC-groups in which normality is a transitive relation

We extend to soluble FC∗ -groups, the class of generalised FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes , Serdica Math. J. 28(3) (2002), 241 254], the characterisation of finite soluble T-groups obtained recently in [G. Kaplan, On T-groups, supersolvable groups and maximal subgroups , Arch. Math. 96 (2011), 19 25].The first author has been supported by the research grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain and FEDER, European Union.Esteban Romero, R.; Vincenzi, G. (2016). On generalised FC-groups in which normality is a transitive relation. Journal of the Australian Mathematical Society. 100(2):192-198. doi:10.1017/S1446788715000397S192198100