Vol. 312, No. 2, 2021

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Cohopfian groups and accessible group classes

Francesco de Giovanni and Marco Trombetti

Vol. 312 (2021), No. 2, 457–475
Abstract

A group G is said to be cohopfian if it is neither trivial nor isomorphic to any of its proper subgroups, and this property is equivalent to the existence of a suitable group class 𝔛 such that G is minimal non-𝔛. If 𝔛 is any group class, the subclass 𝔛 consisting of all groups that are isomorphic to proper subgroups of locally graded minimal non-𝔛 groups is often much smaller than 𝔛. Similarly, if 𝔛prop is the class of all groups isomorphic to proper subgroups of 𝔛-groups, the class 𝔛¯ of all locally graded minimal non-𝔛prop groups may contain many groups which are not in 𝔛. This paper investigates the relation between the classes 𝔛, 𝔛 and 𝔛¯.

Keywords
cohopfian group, cohopfian group class, accessible group class
Mathematical Subject Classification 2010
Primary: 20E34
Milestones
Received: 26 February 2020
Revised: 7 January 2021
Accepted: 3 May 2021
Published: 31 August 2021
Authors
Francesco de Giovanni
Dipartimento di Matematica e Applicazioni
Università degli Studi di Napoli Federico II
Napoli
Italy
Marco Trombetti
Dipartimento di Matematica e Applicazioni
Università degli Studi di Napoli Federico II
Napoli
Italy