Homomorphic encoders of profinite abelian groups I
نویسندگان
چکیده
منابع مشابه
Maximal abelian subgroups of free profinite groups
THEOREM. Let F be the free profinite group on a set X, where \X\ > 2, and let n be a non-empty set of primes. Then F has a maximal abelian subgroup isomorphic to HpEn Zp. The idea of the proof is the following: we show that A — Ylpe7I1p is a free factor of Pa, i.e. fia ^ A *B for some profinite group B. To conclude from this that A is a maximal abelian subgroup of Fa (the general case then foll...
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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: Journal of Pure and Applied Algebra
سال: 2022
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2022.107305