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.
Gharibkhajeh, A., & Doostie, H. (2014). Triple factorization of non-abelian groups by two maximal subgroups. Journal of Algebra and Related Topics, 2(2), 1-9.
MLA
A. Gharibkhajeh; H. Doostie. "Triple factorization of non-abelian groups by two maximal subgroups". Journal of Algebra and Related Topics, 2, 2, 2014, 1-9.
HARVARD
Gharibkhajeh, A., Doostie, H. (2014). 'Triple factorization of non-abelian groups by two maximal subgroups', Journal of Algebra and Related Topics, 2(2), pp. 1-9.
VANCOUVER
Gharibkhajeh, A., Doostie, H. Triple factorization of non-abelian groups by two maximal subgroups. Journal of Algebra and Related Topics, 2014; 2(2): 1-9.
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