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

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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… Click to show full abstract

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.

Keywords: subgroup; solvable groups; groups normalizer; non; non solvable; normalizer every

Journal Title: Communications in Algebra
Year Published: 2018

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