# Weakly totally permutable products and Fitting classes

Document Type: Research Paper

Author

Department of Mathematics and Applied Mathematics, Faculty of Natural and Agricultural Sciences, University of Pretoria

Abstract

It is known that if $G=AB$ is a product of its totally permutable subgroups $A$ and $B$‎, ‎then $G\in \mathfrak{F}$ if and only if $A\in \mathfrak{F}$ and $B\in \mathfrak{F}$ when $\mathfrak{F}$ is a Fischer class containing the class $\mathfrak{U}$ of supersoluble groups‎. ‎We show that this holds when $G=AB$ is a weakly totally permutable product for a particular Fischer class‎, ‎$\mathfrak{F}\diamond \mathfrak{N}$‎, ‎where $\mathfrak{F}$ is a Fitting class containing the class $\mathfrak{U}$ and $\mathfrak{N}$ a class of nilpotent groups‎. ‎We also extend some results concerning the $\mathfrak{U}$-hypercentre of a totally permutable product to a weakly totally permutable product‎.

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