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| Titel: |
Calculating the mislin genus for a certain family of nilpotent groups |
| Auteur: |
Carles, Casacuberta Peter, Hilton |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 19 (1991) nr. 7 pagina's 2051-2069 |
| Jaar: |
1991 |
| Inhoud: |
It is known that the Mislin genus of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. In this paper, we compute explicitly that structure under the following additional assumptions: The torsion subgroup TN is abelian, the epimorphism N→N/TN splits and all automorphisms of TN commute with cinjugation by elements of N. Among the groups satisfying these conditions are all nilpotent split extensions of a finite cyclic group by a finitely free abelian group. We further prove that the function M ↦ M × Nk1k ≥ 2, which is in general a surjective homomorphism from the genus of N onto the genus of Nk, is an isomorphism at least in an imporatnt special case. Applications to the study of non-cancellation phenomena in group theory are given. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 3 van 18 gevonden artikelen
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