3 research outputs found
On finite groups factorised by submodular subgroups
A subgroup of a finite group is submodular in if there is a
subgroup chain such
that is a modular subgroup of for every . We investigate
finite factorised groups with submodular primary (cyclic primary) subgroups in
factors. We indicate a general approach to the description of finite groups
factorised by supersolvable submodular subgroups
On groups with modular Schmidt subgroups
We prove that if every Schmidt subgroup of a group is subnormal or
modular, then is cycli
On -subnormality and submodularity in a finite group
Let be a formation and let be a group. A subgroup of
is -subnormal (submodular) in if there is a
subgroup chain such that for every either is normal in or
( is a modular subgroup of ,
respectively). We prove that a primary subgroup of a group is
submodular in if and only if is -subnormal in
. Here is the class of all supersolvable groups of
square-free exponent. In addition, for a solvable subgroup-closed formation
, every solvable -subnormal subgroup of a
group is contained in the solvable radical of