The p-period of an infinite group.

Título inglés The p-period of an infinite group.
Título español El periodo-p de un grupo infinito.
Autor/es Yining, Xia
Organización Dep. Math. Ohio State Univ., Columbus (Ohio), Estados Unidos
Revista 0214-1493
Publicación 1992, 36 (1): 241-250, 12 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés For Γ a group of finite virtual cohomological dimension and a prime p, the p-period of Γ is defined to be the least positive integer d such that Farrell cohomology groups Hi(Γ; M) and Hi+d(Γ; M) have naturally isomorphic ZΓ modules M.
We generalize a result of Swan on the p-period of a finite p-periodic group to a p-periodic infinite group, i.e., we prove that the p-period of a p-periodic group Γ of finite vcd is 2LCM(|N(áxñ) / C(áxñ)|) if the Γ has a finite quotient whose a p-Sylow subgroup is elementary abelian or cyclic, and the kernel is torsion free, where N(-) and C(-) denote normalizer and centralizer, áxñ ranges over all conjugacy classes of Z/p subgroups. We apply this result to the computation of the p-period of a p-periodic mapping class group. Also, we give an example to illustrate this formula is false without our assumption.
Clasificación UNESCO 120106
Palabras clave español Grupos infinitos ; Grupos periódicos ; Cohomología ; Periodicidad
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