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Abstract
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A group
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
such that
is minimal
non-. If
is any group class,
the subclass
consisting of all groups that are isomorphic to proper subgroups of locally graded minimal
non- groups is often
much smaller than
.
Similarly, if
is the class of all groups isomorphic to proper subgroups of
-groups, the class
of all locally graded
minimal non-
groups may contain many groups which are not in
.
This paper investigates the relation between the classes
,
and
.
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Keywords
cohopfian group, cohopfian group class, accessible group
class
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Mathematical Subject Classification 2010
Primary: 20E34
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Milestones
Received: 26 February 2020
Revised: 7 January 2021
Accepted: 3 May 2021
Published: 31 August 2021
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