Large hereditarily just infinite groups
نویسندگان
چکیده
منابع مشابه
Topological Full Groups of Minimal Subshifts and Just-infinite Groups
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...
متن کاملJust-infinite Groups and Topological Full Groups of Minimal Subshifts
There does not exist an isomorphism-invariant Borel map which selects a just-infinite quotient of each infinite finitely generated group.
متن کاملOn the structure of just infinite profinite groups
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...
متن کاملHereditarily Separable Groups and Monochromatic Uniformization
We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality א1. This can be used, together with a known combinatorial equivalent of the existence of a non-free Whitehead group, to prove that it is consistent that every Whitehead group is free but not every hereditarily separable group is free. We also show that the fact that Z is a p.i.d. with i...
متن کاملStably Just Infinite Rings
We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite provided that the ring is either right noetherian (4.2) or countably generated over a large field (6.4). We give examples to show that, over countable fields...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.03.023