Abstract
We say that the subgroups
G
1
and
G
2
of a group
G
are mutually permutable if
G
1
permutes with every subgroup of
G
2
and
G
2
permutes with every subgroup of
G
1
. Let
G
=
G
1
G
2
…
G
n
be the product of its pairwise permutable subgroups
G
1
,
G
2
,…,
G
n
such that the product
G
i
G
j
is mutually permutable. We investigate the structure of the finite group
G
if special properties of the factors
G
1
,
G
2
,…,
G
n
are known. Our results improve and extend some results of Asaad and Shaalan [1], Ezquerro and Soler-Escrivà [9] and Asaad and Monakhov [3].