ON LOCAL FINITENESS OF VERBAL SUBGROUPS IN RESIDUALLY FINITE GROUPS

2011 ◽  
Author(s):  
P. SHUMYATSKY
Keyword(s):  
Finite Groups ◽  
Residually Finite ◽  
Local Finiteness ◽  
Residually Finite Groups ◽  
Verbal Subgroups

scholarly journals ON LOCAL FINITENESS OF PERIODIC RESIDUALLY FINITE GROUPS

2002 ◽  
Vol 45 (3) ◽  
pp. 717-721 ◽  
Author(s):  
Mahmut Kuzucuoğlu ◽  
Pavel Shumyatsky
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Nilpotent Subgroup ◽  
Subject Classification ◽  
Locally Finite ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Local Finiteness ◽  
Residually Finite Groups

AbstractLet $G$ be a periodic residually finite group containing a nilpotent subgroup $A$ such that $C_G(A)$ is finite. We show that if $\langle A,A^g\rangle$ is finite for any $g\in G$, then $G$ is locally finite.AMS 2000 Mathematics subject classification: Primary 20F50

scholarly journals ON VERBAL SUBGROUPS IN RESIDUALLY FINITE GROUPS

2011 ◽  
Vol 84 (1) ◽  
pp. 159-170 ◽  
Author(s):  
JHONE CALDEIRA ◽  
PAVEL SHUMYATSKY
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Locally Finite ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Verbal Subgroup ◽  
Residually Finite Groups ◽  
Positive Integers ◽  
Verbal Subgroups

AbstractThe following theorem is proved. Let m, k and n be positive integers. There exists a number η=η(m,k,n) depending only on m, k and n such that if G is any residually finite group satisfying the condition that the product of any η commutators of the form [xm,y1,…,yk ] is of order dividing n, then the verbal subgroup of G corresponding to the word w=[xm,y1,…,yk ] is locally finite.

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
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