%0 Journal Article
%T Triple factorization of non-abelian groups by two maximal subgroups
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Gharibkhajeh, A.
%A Doostie, H.
%D 2014
%\ 12/01/2014
%V 2
%N 2
%P 1-9
%! Triple factorization of non-abelian groups by two maximal subgroups
%K Rank
%K Rank-two geometry
%K triple factorization
%K two geometry
%K dihedral groups
%K projective special linear groups
%K projective special linear groups
%R
%X 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.
%U https://jart.guilan.ac.ir/article_62_a4af88eb7a50ab26ce9dd84f84e68652.pdf