The classification of the inverse limits of sequences of free groups of finite rank

2013 ◽  
Vol 45 (4) ◽  
pp. 671-676
Author(s):  
Katsuya Eda ◽  
Jun Nakamura
Keyword(s):  
Finite Rank ◽  
Free Groups ◽  
Inverse Limits

scholarly journals Inverse limits of finite rank free groups

2012 ◽  
Vol 15 (6) ◽  
Author(s):  
Gregory R. Conner ◽  
Curtis Kent
Keyword(s):  
Homomorphic Image ◽  
Free Group ◽  
Finite Rank ◽  
Inverse Limit ◽  
Free Groups ◽  
Inverse System ◽  
Inverse Limits ◽  
Universal Group ◽  
Hawaiian Earring ◽  
Constant System

Abstract.We will show that the inverse limit of finite rank free groups with surjective connecting homomorphism is isomorphic either to a finite rank free group or to a fixed universal group. In other words, any inverse system of finite rank free groups which is not equivalent to an eventually constant system has the universal group as its limit. This universal inverse limit is naturally isomorphic to the first shape group of the Hawaiian earring. We also give an example of a homomorphic image of the Hawaiian earring group which lies in the inverse limit of free groups but is neither a free group nor isomorphic to the Hawaiian earring group.

scholarly journals On the generic type of the free group

2011 ◽  
Vol 76 (1) ◽  
pp. 227-234 ◽  
Author(s):  
Rizos Sklinos
Keyword(s):  
Free Group ◽  
Finite Rank ◽  
Free Groups ◽  
Primitive Elements ◽  
Generic Type

AbstractWe answer a question raised in [9], that is whether the infinite weight of the generic type of the free group is witnessed in Fω. We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not ℵ1-homogeneous.

scholarly journals Towards the complete classification of generalized tent maps inverse limits

2013 ◽  
Vol 160 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Iztok Banič ◽  
Matevž Črepnjak ◽  
Matej Merhar ◽  
Uroš Milutinović
Keyword(s):  
Complete Classification ◽  
Inverse Limits ◽  
Tent Maps

On Torsion-Free Groups of Finite Rank

1984 ◽  
Vol 36 (6) ◽  
pp. 1067-1080 ◽  
Author(s):  
David Meier ◽  
Akbar Rhemtulla
Keyword(s):  
Equivalence Class ◽  
Equivalence Relation ◽  
Finite Rank ◽  
Maximal Element ◽  
Free Groups ◽  
Solvable Groups ◽  
Finitely Generated ◽  
Isolated Subgroup ◽  
Image Position ◽  
Torsion Free

This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for all H ≦ G. Groups possessing the isolator property were discussed in [2]. If we define the relation ∼ on the set of subgroups of a given group G by the rule H ∼ K if and only if , then ∼ is an equivalence relation and every equivalence class has a maximal element which may not be unique. If , we call H an isolated subgroup of G.

AUTOMORPHISMS OF RELATIVELY FREE GROUPS IN THE VARIETY N2A ∧ AN2 ∧ Nc

2001 ◽  
Vol 63 (3) ◽  
pp. 607-622 ◽  
Author(s):  
ATHANASSIOS I. PAPISTAS
Keyword(s):  
Automorphism Group ◽  
Free Group ◽  
Finite Index ◽  
Finite Rank ◽  
Free Groups ◽  
Finite Set ◽  
Tame Automorphism ◽  
Positive Integers ◽  
Relatively Free Group

For positive integers n and c, with n [ges ] 2, let Gn, c be a relatively free group of finite rank n in the variety N2A ∧ AN2 ∧ Nc. It is shown that the subgroup of the automorphism group Aut(Gn, c) of Gn, c generated by the tame automorphisms and an explicitly described finite set of IA-automorphisms of Gn, c has finite index in Aut(Gn, c). Furthermore, it is proved that there are no non-trivial elements of Gn, c fixed by every tame automorphism of Gn, c.

scholarly journals The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

2005 ◽  
Vol 9 (4) ◽  
pp. 1835-1880 ◽  
Author(s):  
Guo-An Diao ◽  
Mark Feighn
Keyword(s):  
Finite Rank ◽  
Free Groups ◽  
Finite Graph
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