Procyclic coverings of commutators in profinite groups
نویسندگان
چکیده
منابع مشابه
Profinite Groups
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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Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2014
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-014-0672-y