Do you want to publish a course? Click here

Subgroup separability in residually free groups

251   0   0.0 ( 0 )
 Added by Henry Wilton
 Publication date 2007
  fields
and research's language is English




Ask ChatGPT about the research

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type $mathrm{FP}_infty$ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.



rate research

Read More

There are limit groups having non-conjugate elements whose images are conjugate in every free quotient. Towers over free groups are freely conjugacy separable.
The congruence subgroup problem for a finitely generated group $Gamma$ asks whether $widehat{Autleft(Gammaright)}to Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(Gammaright)$? Here $hat{X}$ denotes the profinite completion of $X$. In this paper we first give two new short proofs of two known results (for $Gamma=F_{2}$ and $Phi_{2}$) and a new result for $Gamma=Phi_{3}$: 1. $Cleft(F_{2}right)=left{ eright}$ when $F_{2}$ is the free group on two generators. 2. $Cleft(Phi_{2}right)=hat{F}_{omega}$ when $Phi_{n}$ is the free metabelian group on $n$ generators, and $hat{F}_{omega}$ is the free profinite group on $aleph_{0}$ generators. 3. $Cleft(Phi_{3}right)$ contains $hat{F}_{omega}$. Results 2. and 3. should be contrasted with an upcoming result of the first author showing that $Cleft(Phi_{n}right)$ is abelian for $ngeq4$.
Answering a question of Dan Haran and generalizing some results of Aschbacher-Guralnick and Suzuki, we prove that given a set of primes pi, any finite group can be generated by a pi-subgroup and a pi-subgroup. This gives a free product description of a countably generated free profinite group.
A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. It is proved that the fundamental group of a hyperbolic 3-manifold (closed or with cusps) is subgroup conjugacy separable.
132 - Mark Sapir , Iva Spakulova 2009
We prove that with probability tending to 1, a 1-relator group with at least 3 generators and relator of length n is residually finite, virtually residually (finite p)-group for all sufficiently large p, and coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions, bridges and excursions in R^k.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا