scholarly journals Groups with decidable word problem that do not embed in groups with decidable conjugacy problem

2020 ◽  
Author(s):  
Arman Darbinyan
Keyword(s):  
Word Problem ◽  
Conjugacy Problem

scholarly journals Presentations of some classical groups

1975 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M.J. Wicks
Keyword(s):  
Word Problem ◽  
Conjugacy Problem ◽  
Classical Groups

The groups considered are Λ = GL(2, Z), π = SL(2, Z) and Θ = PSL(2, Z). A presentation of Λ is obtained for which the word problem can be solved by a simple intrinsic algorithm. The presentation is modified to display other features of Λ, and to obtain related presentations of Λ and Θ. There is an algorithm which solves the conjugacy problem of Λ.

The co-word problem and the conjugacy problem

2017 ◽  
pp. 256-269
Author(s):  
Derek Holt ◽  
Sarah Rees ◽  
Claas E. Roever
Keyword(s):  
Word Problem ◽  
Conjugacy Problem

COMPRESSED DECISION PROBLEMS FOR GRAPH PRODUCTS AND APPLICATIONS TO (OUTER) AUTOMORPHISM GROUPS

2012 ◽  
Vol 22 (08) ◽  
pp. 1240007 ◽  
Author(s):  
NIKO HAUBOLD ◽  
MARKUS LOHREY ◽  
CHRISTIAN MATHISSEN
Keyword(s):  
Automorphism Group ◽  
Word Problem ◽  
Polynomial Time ◽  
Coxeter Group ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Conjugacy Problem ◽  
Artin Group ◽  
Graph Products ◽  
Direct Corollary

It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a restricted variant of the simultaneous compressed conjugacy problem is polynomial time Turing-reducible to the same problem for the vertex groups. A direct corollary of this result is that the word problem for the outer automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Finally, it is shown that the compressed variant of the ordinary conjugacy problem can be solved in polynomial time for right-angled Artin groups.

Unsolvable Problems in Groups With Solvable Word Problem

1970 ◽  
Vol 22 (4) ◽  
pp. 836-838 ◽  
Author(s):  
James McCool
Keyword(s):  
Word Problem ◽  
Conjugacy Problem ◽  
The Other ◽  
Decision Problems ◽  
Finitely Presented Group ◽  
Other Hand ◽  
Solvable Word Problem ◽  
Finitely Presented ◽  
Effective Procedures ◽  
Solvable Word

Let G be a finitely presented group with solvable word problem. It is of some interest to ask which other decision problems must necessarily be solvable for such a group. Thus it is easy to see that there exist effective procedures to determine whether or not such a group is trivial, or nilpotent of a given class. On the other hand, the conjugacy problem need not be solvable for such a group, for Fridman [5] has shown that the word problem is solvable for the group with unsolvable conjugacy problem given by Novikov [9].

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