Hyper-(rank one) groups |
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| Authors: | Francesco de Giovanni Martin L Newell |
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| Institution: | 1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, via Cintia, Naples, Italy
2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
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| Abstract: | A group $G$ is called a $\mathcal{P }_1$ -group if it has a normal series of finite length whose factors have rank $1$ , while $G$ is an $\mathcal{H }_1$ -group if it has an ascending normal series of the same type. This paper investigates properties of $\mathcal{P }_1$ -groups and $\mathcal{H }_1$ -groups which correspond to known properties of nilpotent and supersoluble groups. |
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