A note on groups whose proper subgroups are quasihamiltonian-by-finite
| Autor: | Francesco de Giovanni, Federica Saccomanno |
|---|---|
| Přispěvatelé: | de Giovanni, Francesco, Saccomanno, Federica |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Group (mathematics) General Mathematics Applied Mathematics 010102 general mathematics 01 natural sciences 010101 applied mathematics Combinatorics Mathematics (all) Quasihamiltonian group 0101 mathematics Algebra over a field Mathematics::Representation Theory Minimal non X-group Mathematics |
| Popis: | If $${\mathfrak {X}}$$ is a class of groups, a group is minimal non- $${\mathfrak {X}}$$ if it is not an $${\mathfrak {X}}$$ -group, but all its proper subgroups belong to $${\mathfrak {X}}$$ . The aim of this paper is to prove that for a periodic locally graded group the property of being minimal non-(quasihamiltonian-by-finite) and that of being minimal non-(abelian-by-finite) are equivalent. Recall here that a group G is called quasihamiltonian if $$XY=YX$$ for all subgroups X and Y of G. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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