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arXiv · 2103.09719

On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup

Ulderico Dardano·Fausto De Mari
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Abstract

We study soluble groups G in which each subnormal subgroup H with infinite rank is commensurable with a normal subgroup, i.e. there exists a normal subgroup N such that the intersection of H and N has finite index in both H and N. We show that if such a G is periodic, then all subnormal subgroups are commensurable with a normal subgroup, provided either the Hirsch-Plotkin radical of G has infinite rank or G is nilpotent-by-abelian (and has infinite rank).

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Ulderico Dardano, Fausto De Mari. 2021-03-17. On groups in which subnormal subgroups of infinite rank are commensurable with some normal subgroup. https://arxiv.org/abs/2103.09719

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