On linear just infinite pro-p groups
نویسندگان
چکیده
منابع مشابه
ON JUST INFINITE PRO-p-GROUPS AND ARITHMETICALLY PROFINITE EXTENSIONS OF LOCAL FIELDS
Let F be a local field of characteristic p > 0 with perfect residue field k. The wild group R = Aut1 F is the group of wild continuous automorphisms {σ : (σ − 1)OF ⊂ MF} of the local field F . A choice of a prime element t of a local field F determines an isomorphism of Aut1 F and the group of formal power series f(t) = t+ a2t 2 + . . . with coefficients from k with respect to the composition (...
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We study subdirect products of free and Demushkin pro-p groups of depth ∞ developing theory similar to the abstract case, see [4]. Furthermore we classify when a subdirect product has homological type FPm for some m ≥ 2, a problem still open for abstract groups for m ≥ 3.
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In [24], confirming a conjecture of Hjorth-Kechris [16], Thomas-Velickovic proved that the isomorphism relation on the space Gfg of finitely generated groups is a universal countable Borel equivalence relation. (Here Gfg denotes the Polish space of finitely generated groups introduced by Grigorchuk [12]; i.e. the elements of Gfg are the isomorphism types of marked groups (G, c ), where G is a f...
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A profinite group G is just infinite if every closed normal subgroup of G is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup H of G, there are only finitely many open normal subgroups of G not contained in H . This extends a result recently established by Barnea, Gavioli, Jaikin-Zapirain, Monti and Scoppola in [1], who proved t...
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There does not exist an isomorphism-invariant Borel map which selects a just-infinite quotient of each infinite finitely generated group.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00024-8