A variety with locally solvable but globally unsolvable word problem

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

scholarly journals Embeddings into groups with only a few defining relations

1974 ◽  
Vol 18 (1) ◽  
pp. 1-7 ◽  
Author(s):  
W. W. Boone ◽  
D. J. Collins
Keyword(s):  
Word Problem ◽  
Finitely Presented Groups ◽  
Fixed Group ◽  
Defining Relations ◽  
Finitely Presented Group ◽  
One Relator Groups ◽  
Finitely Presented ◽  
Unsolvable Word Problem ◽  
Trivial Consequence

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.

On the Word Problem for Orthocomplemented Modular Lattices

1989 ◽  
Vol 41 (6) ◽  
pp. 961-1004 ◽  
Author(s):  
Michael S. Roddy
Keyword(s):  
Word Problem ◽  
Division Ring ◽  
Modular Lattice ◽  
Modular Lattices ◽  
Commutative Field ◽  
Free Modular Lattice ◽  
Finitely Presented ◽  
Unsolvable Word Problem

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.

Simple examples of groups with unsolvable word problem

1969 ◽  
Vol 6 (5) ◽  
pp. 768-775 ◽  
Author(s):  
V. V. Borisov
Keyword(s):  
Word Problem ◽  
Unsolvable Word Problem

Example of a finitely presented group in the variety α5 with the unsolvable word problem

1973 ◽  
Vol 12 (5) ◽  
pp. 327-346 ◽  
Author(s):  
V. N. Remeslennikov
Keyword(s):  
Word Problem ◽  
Finitely Presented Group ◽  
Finitely Presented ◽  
Unsolvable Word Problem

scholarly journals A simple presentation of a group with unsolvable word problem

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

Groups With Two Generators Having Unsolvable Word Problem and Presentations of Mihailova Subgroups of Braid Groups

2016 ◽  
Vol 44 (7) ◽  
pp. 3020-3037
Author(s):  
Xiaofeng Wang ◽  
Guo Li ◽  
Ling Yang ◽  
Hanling Lin
Keyword(s):  
Word Problem ◽  
Braid Groups ◽  
Unsolvable Word Problem

ON THE WORD PROBLEM IN PERIODIC GROUP VARIETIES

1991 ◽  
Vol 01 (01) ◽  
pp. 115-126 ◽  
Author(s):  
M. V. SAPIR
Keyword(s):  
Word Problem ◽  
Periodic Group ◽  
Group Variety ◽  
Finitely Based ◽  
Burnside Problem ◽  
Unsolvable Word Problem

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.

scholarly journals Computability of Følner sets

2017 ◽  
Vol 27 (07) ◽  
pp. 819-830 ◽  
Author(s):  
Matteo Cavaleri
Keyword(s):  
Word Problem ◽  
Finitely Generated ◽  
Amenable Groups ◽  
Finitely Generated Groups ◽  
Distortion Functions ◽  
Solvable Word Problem ◽  
Følner Sets ◽  
Finitely Presented ◽  
Unsolvable Word Problem ◽  
Solvable Word

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.

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