University of Guilan Journal of Algebra and Related Topics 2345-3931 2 2 2014 12 01 Triple factorization of non-abelian groups by two maximal subgroups 1 9 62 EN A. Gharibkhajeh Islamic Azad University H. Doostie Islamic Azad University Journal Article 2014 08 03 The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$ for their triple factorizations by finding certain suitable maximal subgroups, which these subgroups are define with original generators of these groups. The related rank-two coset geometries motivate us to define the rank-two coset geometry graphs which could be of intrinsic tool on the study of triple factorization of non-abelian groups. Rank Rank-two geometry triple factorization two geometry dihedral groups projective special linear groups projective special linear groups https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf