scholarly journals Ascending HNN extensions of residually finite groups can be non-Hopfian and can have very few finite quotients

2002 ◽  
Vol 166 (1-2) ◽  
pp. 191-202 ◽  
Author(s):  
Mark Sapir ◽  
Daniel T. Wise
Keyword(s):  
Finite Groups ◽  
Residually Finite ◽  
Hnn Extensions ◽  
Residually Finite Groups ◽  
Finite Quotients

A property of finitely generated residually finite groups

1976 ◽  
Vol 15 (3) ◽  
pp. 347-350 ◽  
Author(s):  
P.F. Pickel
Keyword(s):  
Finite Group ◽  
Homomorphic Image ◽  
Finite Groups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Isomorphism Classes ◽  
Residually Finite Groups ◽  
Finite Quotients ◽  
Relatively Free Group

Let F(G) denote the set of isomorphism classes of finite quotients of the group G. We say that groups G and H have isomorphic finite quotients (IFQ) if F(G) = F(H). In this note, we show that a finitely generated residually finite group G cannot have the same finite quotients as a proper homomorphic image (G is IFQ hopfian). We then obtain some results on groups with the same finite quotients as a relatively free group.

scholarly journals On Groups of Automorphisms of Residually Finite Groups

2000 ◽  
Vol 231 (2) ◽  
pp. 561-573
Author(s):  
Ulderico Dardano ◽  
Bettina Eick ◽  
Martin Menth
Keyword(s):  
Finite Groups ◽  
Residually Finite ◽  
Residually Finite Groups ◽  
Groups Of Automorphisms

scholarly journals An uncountable family of finitely generated residually finite groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hip Kuen Chong ◽  
Daniel T. Wise
Keyword(s):  
Free Group ◽  
Finite Groups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Uncountable Family ◽  
Residually Finite Groups ◽  
Rank 2

Abstract We study a family of finitely generated residually finite groups. These groups are doubles F 2 * H F 2 F_{2}*_{H}F_{2} of a rank-2 free group F 2 F_{2} along an infinitely generated subgroup 𝐻. Varying 𝐻 yields uncountably many groups up to isomorphism.

Actions and Invariants of Residually Finite Groups: Asymptotic Methods

2010 ◽  
pp. 2335-2391
Author(s):  
Miklós Abért ◽  
Damien Gaboriau ◽  
Fritz Grunewald
Keyword(s):  
Finite Groups ◽  
Asymptotic Methods ◽  
Residually Finite ◽  
Residually Finite Groups

scholarly journals Hydra group doubles are not residually finite

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Kristen Pueschel
Keyword(s):  
Finite Groups ◽  
Recursive Function ◽  
Dehn Functions ◽  
Residually Finite ◽  
Residually Finite Groups ◽  
Finitely Presented

AbstractIn 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function

An embedding theorem for certain residually finite groups

1996 ◽  
Vol 67 (3) ◽  
pp. 177-182 ◽  
Author(s):  
J. S. Wilson ◽  
P. A. Zalesskii
Keyword(s):  
Finite Groups ◽  
Embedding Theorem ◽  
Residually Finite ◽  
Residually Finite Groups
Sign in / Sign up

Export Citation Format

Share Document