相关论文: On hereditarily just infinite profinite groups obt…

We study a family of hereditarily just infinite profinite groups obtained by iterated wreath products introduced by J. Wilson in 2010. We find explicit generators for this family in a number of cases using combinatorial methods. We then…

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be…

We study infinitely iterated wreath products of finite permutation groups with respect to product actions. In particular, we prove that, for every non-empty class of finite simple groups $\mathcal{X}$, there exists a finitely generated…

We show that the group constructed in the 2004 paper 'A 2-generated just-infinite profinite group which is not positively finitely generated' by A. Lucchini is in fact hereditarily just infinite and contains every countably based profinite…

We determine the lower rank of the direct product of finitely many hereditarily just infinite profinite groups of finite lower rank.

We give criteria on an inverse system of finite groups that ensure the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'universal' in that all (hereditarily) just infinite profinite groups arise…

We show that there are hereditarily just infinite groups of any subgroup growth type between $n$ and $n^{\log n}$. This is obtained calculating the subgroup growth type of a family of hereditarily just infinite profinite groups obtained via…

We construct an uncountable family of 3-generated residually finite just-infinite groups with isomorphic profinite completions. We also show that word growth rate is not a profinite property.

Finitely generated (non-abelian) free metabelian pro-p groups, and wreath products of f.g. free abelian pro-p groups, are all finitely axiomatizable in the class of all profinite groups.

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

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…

Just infinite groups play a significant role in profinite group theory. For each $c \geq 0$, we consider more generally JNN$_c$F profinite (or, in places, discrete) groups that are Fitting-free; these are the groups $G$ such that every…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

We introduce a class $\A$ of finitely generated residually finite accessible groups with some natural restriction on one-ended vertex groups in their JSJ-decompositions. We prove that the profinite completion of groups in $\A$ almost…

A residually finite (profinite) group $G$ is just infinite if every non-trivial (closed) normal subgroup of $G$ is of finite index. This paper considers the problem of determining whether a (closed) subgroup $H$ of a just infinite group is…

It is proved that every finitely generated profinite group with fewer than $2^{\aleph_0}$ conjugacy classes of elements of infinite order is finite

We construct an uncountable family of periodic locally soluble groups which are hereditarily just infinite. We also show that the associated full C*-algebra C*(G) is just infinite for many groups $G$ in this family.

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.

We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type $\mathrm{F}_\infty$ (in particular, they are finitely presented) that act faithfully on the circle by orientation-preserving homeomorphisms,…

Let $(G_n,X_n)$ be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath product $...\wr G_2\wr G_1$ is topologically finitely generated if…