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2018•Journal of Algebra and Its ApplicationsRequires access

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

Jiangtao Shi

Open publisher page 5 citations

Abstract

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 [Formula: see text] is a TI-subgroup or a subnormal subgroup, then every non-abelian subgroup of [Formula: see text] must be subnormal in [Formula: see text]. We also show that the non-cyclic subgroups have the same property.

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What this paper is about

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 [Formula: see text] is a TI-subgroup or a subnormal subgroup, then every non-abelian subgroup of [Formula: see text] must be subnormal in [Formula: see text]. We also show that the non-cyclic subgroups have the same property.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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 [Formula: see text] is a TI-subgroup or a subnormal subgroup, then every non-abelian subgroup of [Formula: see text] must be subnormal in [Formula: see text]. We also show that the non-cyclic subgroups have the same property.

Key concepts: Characteristic subgroup, Mathematics, Torsion subgroup, Omega and agemo subgroup, Commutator subgroup, Fitting subgroup, Index of a subgroup, Maximal subgroup

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