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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