The transfer in mod-p group cohomology between Σ_p \int Σ_{p^{n-1}}, Σ_{p^{n-1}} \int Σ_p and Σ_{p^n}

dc.creatorKechagias, Nondas E.
dc.date2009-03-30
dc.date.accessioned2026-07-07T12:58:12Z
dc.date.available2026-07-07T12:58:12Z
dc.descriptionIn this work we compute the induced transfer map: $$\barτ^\ast: \func{Im}(res^\ast:H^\ast(G) \to H^\ast(V)) \to \func{Im}(res^\ast: H^\ast (Σ_{p^n}) \to H^\ast(V))$$ in $\func{mod}p$-cohomology. Here $Σ_{p^{n}}$ is the symmetric group acting on an $n$-dimensional $\mathbb F_p$ vector space $V$, $G=Σ_{p^{n},p}$ a $p$-Sylow subgroup, $Σ_{p^{n-1}}\int Σ_{p}$, or $Σ_{p}\int Σ_{p^{n-1}}$. Some answers are given by natural invariants which are related to certain parabolic subgroups. We also compute a free module basis for certain rings of invariants over the classical Dickson algebra. This provides a computation of the image of the appropriate restriction map. Finally, if $ ξ:\func{Im}(res^\ast:H^\ast(G) \to H^\ast(V)) \to \func{Im}(res^\ast}: H^\ast(Σ_{p^n}) \to H^\ast(V)) $ is the natural epimorphism, then we prove that $\barτ^\ast=ξ$ in the ideal generated by the top Dickson algebra generator.
dc.description24, pages
dc.identifierhttps://arxiv.org/abs/0903.5239
dc.identifierhttp://arxiv.org/abs/0903.5239
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225161
dc.subjectAlgebraic Topology
dc.subjectK-Theory and Homology
dc.subject55S10, 20J05, 18G10
dc.titleThe transfer in mod-p group cohomology between Σ_p \int Σ_{p^{n-1}}, Σ_{p^{n-1}} \int Σ_p and Σ_{p^n}
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