FINITE TRIFACTORISED GROUPS AND -DECOMPOSABILITY

We derive some structural properties of a trifactorised finite group $G=AB=AC=BC$ , where $A$ , $B$ , and $C$ are subgroups of $G$ , provided that $A=A_{\unicode[STIX]{x1D70B}}\times A_{\unicode[STIX]{x1D70B}^{\prime }}$ and $B=B_{\unicode[STIX]{x1D70B}}\times B_{\unicode[STIX]{x1D70B}^{\prime }}$ are $\unicode[STIX]{x1D70B}$ -decomposable groups, for a set of primes $\unicode[STIX]{x1D70B}$ .