The p-period of an infinite group.

Yining, Xia. "The p-period of an infinite group.." Publicacions Matemàtiques 36.1 (1992): 241-250. <http://eudml.org/doc/41153>.

@article{Yining1992,
abstract = {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(〈x〉) / C(〈x〉)|) 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, 〈x〉 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.},
author = {Yining, Xia},
journal = {Publicacions Matemàtiques},
keywords = {Grupos infinitos; Grupos periódicos; Cohomología; Periodicidad; virtual cohomological dimension; subgroup of finite index; Farrell cohomology; Tate cohomology; -period; -primary components; - periodic group; mapping class groups},
language = {eng},
number = {1},
pages = {241-250},
title = {The p-period of an infinite group.},
url = {http://eudml.org/doc/41153},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Yining, Xia
TI - The p-period of an infinite group.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 241
EP - 250
AB - 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(〈x〉) / C(〈x〉)|) 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, 〈x〉 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.
LA - eng
KW - Grupos infinitos; Grupos periódicos; Cohomología; Periodicidad; virtual cohomological dimension; subgroup of finite index; Farrell cohomology; Tate cohomology; -period; -primary components; - periodic group; mapping class groups
UR - http://eudml.org/doc/41153
ER -