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Abstract
A subgroup X of a group G is strongly inert if the index | ⟨ X, X g ⟩: X| is finite for all elements g ∈ G, and a group is strongly inertial if all its subgroups are strongly inert. This article investigates the structure of strongly inertial groups. In particular, strongly inertial groups which are either finitely generated or minimax are completely classified. Moreover, groups in which many subgroups are strongly inert are studied.
2010 Mathematics Subject Classification:
ACKNOWLEDGEMENT
This research was carried out while the fourth author was a visitor at the “Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II.” He is grateful for the excellent hospitality.
Dedicated to Hermann Heineken on the occasion of his 75th birthday.
Notes
Communicated by S. Sehgal.