unsolvable word problem
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2017 ◽  
Vol 27 (07) ◽  
pp. 819-830 ◽  
Author(s):  
Matteo Cavaleri

We define the notion of computability of Følner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich groups, finitely presented solvable groups with unsolvable Word Problem, have computable Følner sets. We also prove computability of Følner sets for extensions — with subrecursive distortion functions — of amenable groups with solvable Word Problem by finitely generated groups with computable Følner sets. Moreover, we obtain some known and some new upper bounds for the Følner function for these particular extensions.



2016 ◽  
Vol 44 (7) ◽  
pp. 3020-3037
Author(s):  
Xiaofeng Wang ◽  
Guo Li ◽  
Ling Yang ◽  
Hanling Lin


1996 ◽  
Vol 35 (3) ◽  
pp. 420-424 ◽  
Author(s):  
S. Crvenković ◽  
D. Delić


1991 ◽  
Vol 01 (01) ◽  
pp. 115-126 ◽  
Author(s):  
M. V. SAPIR

It is shown that there is a finitely based periodic group variety with unsolvable word problem. This uses the solution by Novikov and Adian of the Burnside problem and solves a subsequent problem raised by Adian and Makanin.



1989 ◽  
Vol 41 (6) ◽  
pp. 961-1004 ◽  
Author(s):  
Michael S. Roddy

In [16] Freese showed that the word problem for the free modular lattice on 5 generators is unsolvable. His proof makes essential use of Mclntyre's construction of a finitely presented field with unsolvable word problem [30]. (We follow Cohn [7] in calling what is commonly called a division ring a field, and what is commonly called a field a commutative field.) In this paper we will use similar ideas to obtain unsolvability results for varieties of modular ortholattices. The material in this paper is fairly wide ranging, the following are recommended as reference texts.



1986 ◽  
Vol 30 (2) ◽  
pp. 230-234 ◽  
Author(s):  
Donald J. Collins




1974 ◽  
Vol 18 (1) ◽  
pp. 1-7 ◽  
Author(s):  
W. W. Boone ◽  
D. J. Collins

It is a trivial consequence of Magnus' solution to the word problem for one-relator groups [9] and the existence of finitely presented groups with unsolvable word problem [4] that not every finitely presented group can be embedded in a one-relator group. We modify a construction of Aanderaa [1] to show that any finitely presented group can be embedded in a group with twenty-six defining relations. It then follows from the well-known theorem of Higman [7] that there is a fixed group with twenty-six defining relations in which every recursively presented group is embedded.



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