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On the complexity of intersection and conjugacy problems in free groups

1984
*
Theoretical Computer Science
*

Having a Nielsen reduced set

doi:10.1016/0304-3975(84)90046-x
fatcat:qkdvbm6v5faupp6luyogzhuy5y
*of*generators for subgroups H*and*K*one*can solve a Ict*of*intersectlon*and**conjugacy**problems**in*polynomial time*in*a uniform way. ... Nielsen type arguments have been used to prove some*problems**in**free**group*? (e.g.,*the*generalized word*problem*) [2] to be P-complete.*In*this paper we extend this approach. ... As by-product a new proof is given that*the**free**groups*have*the*Howson property.*The*second*problem*is*the**conjugacy**problem**of*Moldavanskii. ...##
###
Detecting conjugacy stability of subgroups in certain classes of groups
[article]

2020
*
arXiv
*
pre-print

*In*this paper we consider

*the*

*conjugacy*stability property

*of*subgroups

*and*provide effective procedures to solve

*the*

*problem*

*in*several classes

*of*

*groups*. ...

*In*particular, we start with

*free*

*groups*, that is, we give an effective procedure to find out if a finitely generated subgroup

*of*a

*free*

*group*is

*conjugacy*stable. ... We would like to thank Alexei Miasnikov for suggesting to take a look at

*the*

*conjugacy*stability

*problem*

*in*

*free*

*groups*. ...

##
###
Computational complexity and the conjugacy problem

2017
*
Computability - The Journal of the Assosiation
*

We also consider

doi:10.3233/com-160060
fatcat:h3c3ebcaunaedom4czsgyw3a2q
*the**complexity*relationship*of**the*"half-*conjugacy*"*problem*to*the**conjugacy**problem*. ...*The**conjugacy**problem*for a finitely generated*group*G is*the*two-variable*problem**of*deciding for an arbitrary pair (u,v)*of*elements*of*G, whether or not u is conjugate to v*in*G. ...*The**complexity**of*an individual*conjugacy**problem*depends*on**the*fixed element u 0 ,*and*its*complexity*may be much less than that*of**the**conjugacy**problem**in*G. ...##
###
Page 6176 of Mathematical Reviews Vol. , Issue 93k
[page]

1993
*
Mathematical Reviews
*

a

*conjugacy**of**the*two*groups**in*Isom(H”). ... For a 2-*complex*K*one*obtains a presentation Px*of*its funda- mental*group**in**the*standard way:*the*generators correspond to*the*1-cells*in**the*complement*of*a maximal tree*in**the*1-skeleton,*and**the*relations ...##
###
Algorithmic Problems in Group Theory (Dagstuhl Seminar 19131)

2019
*
Dagstuhl Reports
*

*On*

*one*hand,

*groups*played an important rule

*in*many developments

*in*

*complexity*theory

*and*automata theory. ...

*On*

*the*other hand, concepts from these computer science fields as well as efficient algorithms, cryptography,

*and*data compression led to

*the*formulation

*of*new questions

*in*

*group*theory. ... Zametki, 25(6):811-824, 956, 1979. 3.5

*On*

*the*

*intersection*

*problem*for

*free*-abelian by

*free*

*groups*Jordi Delgado Rodríguez

*and*Enric Ventura Capell Main reference Jordi Delgado, "Extensions

*of*

*Free*

*Groups*...

##
###
Polynomial time conjugacy in wreath products and free solvable groups
[article]

2010
*
arXiv
*
pre-print

We prove that

arXiv:1011.5931v1
fatcat:jrakkcgcdfawlffzu42n3t4k34
*the**complexity**of**the**Conjugacy**Problems*for wreath products*and*for*free*solvable*groups*is decidable*in*polynomial time. ... Using this result*and*properties*of**the*Magnus embedding, we show that*the**Conjugacy**and**Conjugacy*Search*Problems**in**free*solvable*groups*are computable*in*polynomial time. ... Introduction*In*this paper we attack*the*computational*complexity**of**the**Conjugacy**and**Conjugacy*Search*Problems**in**free*solvable*groups*. ...##
###
Orbit decidability and the conjugacy problem for some extensions of groups
[article]

2007
*
arXiv
*
pre-print

*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*... Also, we give an easy way

*of*constructing

*groups*

*of*

*the*form Z^4 F_n

*and*F_3 F_n with unsolvable

*conjugacy*

*problem*. ... We formulate

*the*question for

*free*

*and*

*free*abelian

*groups*because, if

*one*allows an arbitrary ambient F , then

*the*answer is negative: consider Collins-Miller example

*of*a finitely presented

*group*G with ...

##
###
Orbit decidability and the conjugacy problem for some extensions of groups

2009
*
Transactions of the American Mathematical Society
*

*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*... Also, we give an easy way

*of*constructing

*groups*

*of*

*the*form Z 4 Fn

*and*F 3 Fn with unsolvable

*conjugacy*

*problem*. ...

*The*first named author is partially supported by

*the*INTAS grant N 03-51-3663

*and*by

*the*grant

*Complex*integration projects

*of*SB RAS N 1.9. ...

##
###
Page 3982 of Mathematical Reviews Vol. , Issue 86i
[page]

1986
*
Mathematical Reviews
*

(D-KSRL); Madlener, K. 86i:20053
(D-KSRL)

*On**the**complexity**of**intersection**and**conjugacy**problems**in**free**groups*. Theoret. Comput. Sci. 32 (1984), no. 3, 279-295. ... Having a Nielsen reduced set*of*generators for subgroups H*and*K,*one*can solve a lot*of**intersection**and**conjugacy**problems**in*polynomial time*in*a uniform way. ...##
###
Integration and conjugacy in knot theory
[article]

2005
*
arXiv
*
pre-print

*In*particular we study

*the*relationship between known solutions from small cancellation theory

*and*normal surface theory for

*the*word

*and*

*conjugacy*

*problems*

*of*

*the*

*groups*

*of*(prime) alternating links. ... This thesis consists

*of*three self-contained chapters.

*The*first two concern quantum invariants

*of*links

*and*three manifolds

*and*

*the*third contains results

*on*

*the*word

*problem*for link

*groups*. ... It is

*the*

*free*product

*of*

*the*Dehn presentation

*of*L

*and*

*the*infinite cyclic

*group*. Therefore, solving

*the*

*conjugacy*(

*and*word)

*problem*for

*the*augmented link

*group*solves it for

*the*link

*group*. ...

##
###
Page 1111 of Mathematical Reviews Vol. 55, Issue 4
[page]

1978
*
Mathematical Reviews
*

A

*group*G is*the*direct sum*of**the*R-*complexes*R,(i € J) if G is*the*set-theoretical union*of**the*R,’s*and*, for each i € J, R,*intersected*with*the*join (*in*Lg)*of**the*remaining*ones*is Z. ...*The*first*group*is described*in**the*notation*of**the*second author [*On**group*theoretic*problems**and*their classification, Ann.*of*Math. ...##
###
Page 4471 of Mathematical Reviews Vol. , Issue 83k
[page]

1983
*
Mathematical Reviews
*

P. 83k:20036 Estimates

*of**the*degree*of**complexity**of*an algorithm for solving*the*word*problem**and**the**conjugacy**problem*for a class*of**groups*. ...*The*author, by constructing a suitable Turing machine, gives upper bounds for*the*degree*of**complexity**of*Dehn’s algorithms for*the*word*and**conjugacy**problems*for small cancellation*groups*. ...##
###
THE CONJUGACY PROBLEM IN AMALGAMATED PRODUCTS I: REGULAR ELEMENTS AND BLACK HOLES

2007
*
International journal of algebra and computation
*

We discuss

doi:10.1142/s0218196707003652
fatcat:67q53fzxlrhchfrc5jw3mmbjxm
*the*time*complexity**of**the*word*and**conjugacy**problems*for*free*products G = A C B*of**groups*A*and*B with amalgamation over a subgroup C. ... We stratify*the*set*of*elements*of*G with respect to*the**complexity**of**the*word*and**conjugacy**problems**and*show that for*the*generic stratum*the**conjugacy*search*problem*is decidable under some reasonable ...*The*third author was supported by EPSRC grant GR/R29451*and*by RFFI grants 02-01-00192*and*05-01-00057. ...##
###
Morse theory and conjugacy classes of finite subgroups
[article]

2007
*
arXiv
*
pre-print

We also construct examples

arXiv:0709.3802v1
fatcat:el6lgq22pragpi5ascg374t54u
*of**groups**of*type F_n inside mapping class*groups*, Aut(F),*and*Out(F) which have infinitely many*conjugacy*classes*of*finite-order elements. ... Unlike previous examples (which were based*on*right-angled Artin*groups*) our ambient CAT(0)*group*does not contain any rank 3*free*abelian subgroups. ... solves*Problem*3.10*in*[9] ),*in*Aut(F k ),*and*Out(F k ), where*the**free**group*has sufficiently high rank. ...##
###
Key-agreement based on automaton groups
[article]

2019
*
arXiv
*
pre-print

subgroup

arXiv:1905.03124v1
fatcat:ionugguliba4zhwlt22vcb5imq
*of**the*affine*group*with*the*unsolvable*conjugacy**problem*... We suggest several automaton*groups*as key-agreement platforms for Anshl-Anshel-Goldfeld metascheme, they include Grigorchuk*and*universal Grigorchuk*groups*, Hanoi 3-Towers*group*, Basilica*group**and*a ... )*and*is grateful to Max-Planck Institut fuer Mathematik, Bonn during staying*in*which*the*paper was conceived. ...
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