We study groups in which the non-abelian subgroups fall into finitely many isomorphic classes. We prove that a locally generalized radical group with this property is abelian-by-finite and reduced minimax. The same conclusion holds for locally generalized coradical groups. Here a generalized radical group is a group with an ascending series whose factors are either locally nilpotent or locally finite, and a generalized coradical group is a group with a descending series whose factors are either locally nilpotent or locally finite.
"Groups with finitely many isomorphic classes of non-abelian subgroups"
P. Longobardi;M. Maj;
2018
Abstract
We study groups in which the non-abelian subgroups fall into finitely many isomorphic classes. We prove that a locally generalized radical group with this property is abelian-by-finite and reduced minimax. The same conclusion holds for locally generalized coradical groups. Here a generalized radical group is a group with an ascending series whose factors are either locally nilpotent or locally finite, and a generalized coradical group is a group with a descending series whose factors are either locally nilpotent or locally finite.File in questo prodotto:
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Groups with finitely many isomorphic classes of non-abelian subgroups.pdf
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