TY - JOUR
A2 - Buskes, G.
A2 - Asaad, M.
A2 - Mason, G.
A2 - Vinet, L.
AU - Hijazi, Rola A.
PY - 2011
DA - 2011/09/07
TI - Mutually Permutable Products of Finite Groups
SP - 867082
VL - 2011
AB - Let G be a finite group and G_{1}, G_{2} are two subgroups of G. Wesay that G_{1} and G_{2} are mutually permutable if G_{1} is permutable with everysubgroup of G_{2} and G_{2} is permutable with every subgroup of G_{1}. We provethat if G=G1G2=G1G3=G2G3 is the product of three supersolvable subgroups G_{1}, G_{2}, and G_{3}, where G_{i} and G_{j} are mutually permutable for all iand j with i≠j and the Sylow subgroups of G are abelian, then G is supersolvable. As a corollary of this result, we also prove that if G possesses threesupersolvable subgroups Gi (i=1,2,3) whose indices are pairwise relativelyprime, and G_{i} and G_{j} are mutually permutable for all i and j with i≠j, thenG is supersolvable.
SN - null
UR - https://doi.org/10.5402/2011/867082
DO - 10.5402/2011/867082
JF - ISRN Algebra
PB - International Scholarly Research Network
KW -
ER -