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2017•Communications in AlgebraRequires access

Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal

Jianji Cao, Xiuyun Guo, K. P. Shum

Open publisher page 2 citations

Abstract

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.

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What this paper is about

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

It is well known that the normality of subgroups plays an important part in the research of group theory. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper we mainly investigate the structure of non-solvable groups in which the normalizer of every non-normal cyclic subgroup is a maximal subgroup, and finally the classification for this kind of groups is given.

Key concepts: Mathematics, Centralizer and normalizer, Maximal subgroup, Solvable group, Fitting subgroup, Characteristic subgroup, Index of a subgroup, Normality

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