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Minimal non self dual groups. (English) Zbl 1332.20013

Authors’ summary: A group \(G\) is self dual if every subgroup of \(G\) is isomorphic to a quotient of \(G\) and every quotient of \(G\) is isomorphic to a subgroup of \(G\). It is minimal non-self dual if every proper subgroup of \(G\) is self dual but \(G\) is not self dual. In this paper the structure of minimal non self dual groups is determined.

MSC:

20D15 Finite nilpotent groups, \(p\)-groups
20D30 Series and lattices of subgroups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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