20 research outputs found
Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups
A presentation of a group with two generators having unsolvable word problem and an explicit countable presentation of Mihailova subgroup of F_2×F_2 with finite number of generators are given. Where Mihailova subgroup of F_2×F_2 enjoys the unsolvable subgroup membership problem.One then can use the presentation to create entities\u27 private key in a public key cryptsystem
A recursive presentation for Mihailova's subgroup
We give an explicit recursive presentation for Mihailova's subgroup of
corresponding to a finite, concise and Peiffer aspherical
presentation . This partially answers a
question of R.I. Grigorchuk, [8, Problem 4.14]. As a corollary, we construct a
finitely generated recursively presented orbit undecidable subgroup of
.Comment: 9 page
Orbit decidability and the conjugacy problem for some extensions of groups
Given a short exact sequence of groups with certain conditions, 1 ? F ? G ? H ? 1, weprove that G has solvable conjugacy problem if and only if the corresponding action subgroupA 6 Aut(F) is orbit decidable. From this, we deduce that the conjugacy problem is solvable,among others, for all groups of the form Z2?Fm, F2?Fm, Fn?Z, and Zn?A Fm with virtually solvable action group A 6 GLn(Z). Also, we give an easy way of constructing groups of the form Z4?Fn and F3?Fn with unsolvable conjugacy problem. On the way, we solve the twisted conjugacy problem for virtually surface and virtually polycyclic groups, and give an example of a group with solvable conjugacy problem but unsolvable twisted conjugacy problem. As an application, an alternative solution to the conjugacy problem in Aut(F2) is given
Orbit decidability and the conjugacy problem for some extensions of groups
Given a short exact sequence of groups with certain conditions, , we prove that has solvable conjugacy problem if and only if
the corresponding action subgroup is orbit decidable. From
this, we deduce that the conjugacy problem is solvable, among others, for all
groups of the form , , , and with virtually solvable action
group . Also, we give an easy way of constructing
groups of the form and with
unsolvable conjugacy problem. On the way, we solve the twisted conjugacy
problem for virtually surface and virtually polycyclic groups, and give an
example of a group with solvable conjugacy problem but unsolvable twisted
conjugacy problem. As an application, an alternative solution to the conjugacy
problem in is given
A recursive presentation for Mihailova's subgroup
"Vegeu el resum a l'inici del document del fitxer adjunt"
A recursive presentation for Mihailova's subgroup
We give an explicit recursive presentation for Mihailova's sub-
group M(H) of Fn Fn corresponding to a nite, concise and Pei er aspherical
presentation H = hx1; : : : ; xn jR1; : : : ;Rmi. This partially answers a question
of R.I. Grigorchuk, [8, Problem 4.14]. As a corollary, we construct a nitely
generated recursively presented orbit undecidable subgroup of Aut(F3)Postprint (published version
The subgroup identification problem for finitely presented groups
We introduce the subgroup identification problem, and show that there is a
finitely presented group G for which it is unsolvable, and that it is uniformly
solvable in the class of finitely presented locally Hopfian groups. This is
done as an investigation into the difference between strong and weak effective
coherence for finitely presented groups.Comment: 11 pages. This is the version submitted for publicatio
Orbit decidability and the conjugacy problem for some extensions of groups
"Vegeu el resum a l'inici del document del fitxer adjunt"