Finite groups in which every non-abelian subgroup is a TI-subgroup or a subnormal subgroup

摘要

It is known that a TI-subgroup of a finite group may not be a subnormal subgroup and a subnormal subgroup of a finite group may also not be a TI-subgroup. For the non-abelian subgroups, we prove that if every non-abelian subgroup of a finite group G is a TI-subgroup or a subnormal subgroup, then every non-abelian subgroup of G must be subnormal in G. We also show that the non-cyclic subgroups have the same property.