منابع مشابه
On the construction of permutation complexes for profinite groups
In [5], Goerss, Henn, Mahowald and Rezk consider the special extended Morava stabilizer group G2 = S2 o Gal at the prime 3 and construct an exact sequence of compact modules 0→ Ind 1 2 G24 Ẑ3 → Ind G2 SD16 Ẑ3(χ)→ Ind G2 SD16 Ẑ3(χ)→ Ind G2 G24 Ẑ3 → Ẑ3 → 0, where G24 is a subgroup of order 24 etc, and Ẑ3(χ) is a copy of Ẑ3 on which SD16 acts via a character χ : SD16 → {±1}. They then use this to ...
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We investigate the continuous cohomology of infinite permutation groups on modules whose topology is profinite. To obtain acyclics we expand the class of modules to include those which are directed unions of their profinite submodules. As an application we give a criterion which implies finiteness of the continuous cohomology groups on finitely generated profinite modules for some familiar perm...
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γ = c0 + c1p+ c2p + · · · = (. . . c3c2c1c0)p, with ci ∈ Z, 0 ≤ ci ≤ p− 1, called the digits of γ. This ring has a topology given by a restriction of the product topology—we will see this below. The ring Zp can be viewed as Z/pZ for an ‘infinitely high’ power n. This is a useful idea, for example, in the study of Diophantine equations: if such an equation has a solution in the integers, then it...
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A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2007
ISSN: 0010-2571
DOI: 10.4171/cmh/83