Geodesic
The conjugacy problem for groups, and Higman embeddings
Ol’shanskii, A.1 ; Sapir, M.2
1 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, and Mechanics-Mathematics Department, Chair of Higher Algebra, Moscow State University, Moscow, Russia
2 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 40-50.

Voir la notice de l'article provenant de la source American Mathematical Society

For every finitely generated recursively presented group ${\mathcal G}$ we construct a finitely presented group ${\mathcal H}$ containing ${\mathcal G}$ such that ${\mathcal G}$ is (Frattini) embedded into ${\mathcal H}$ and the group ${\mathcal H}$ has solvable conjugacy problem if and only if ${\mathcal G}$ has solvable conjugacy problem. Moreover, ${\mathcal G}$ and ${\mathcal H}$ have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D. Collins.
DOI : 10.1090/S1079-6762-03-00110-0

Ol’shanskii, A. 1 ; Sapir, M. 2

1 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240, and Mechanics-Mathematics Department, Chair of Higher Algebra, Moscow State University, Moscow, Russia
2 Mathematics Department, Vanderbilt University, Nashville, Tennessee 37240 
@article{ERAAMS_2003_09_a5,
     author = {Ol{\textquoteright}shanskii, A. and Sapir, M.},
     title = {The conjugacy problem for groups, and {Higman} embeddings},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {40--50},
     publisher = {mathdoc},
     volume = {09},
     year = {2003},
     doi = {10.1090/S1079-6762-03-00110-0},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00110-0/}
}
TY  - JOUR
AU  - Ol’shanskii, A.
AU  - Sapir, M.
TI  - The conjugacy problem for groups, and Higman embeddings
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2003
SP  - 40
EP  - 50
VL  - 09
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00110-0/
DO  - 10.1090/S1079-6762-03-00110-0
ID  - ERAAMS_2003_09_a5
ER  - 
%0 Journal Article
%A Ol’shanskii, A.
%A Sapir, M.
%T The conjugacy problem for groups, and Higman embeddings
%J Electronic research announcements of the American Mathematical Society
%D 2003
%P 40-50
%V 09
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00110-0/
%R 10.1090/S1079-6762-03-00110-0
%F ERAAMS_2003_09_a5
Ol’shanskii, A.; Sapir, M. The conjugacy problem for groups, and Higman embeddings. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 40-50. doi : 10.1090/S1079-6762-03-00110-0. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00110-0/

[1] Clapham, C. R. J. An embedding theorem for finitely generated groups Proc. London Math. Soc. (3) 1967 419 430

[2] Collins, Donald J. Conjugacy and the Higman embedding theorem 1980 81 85

[3] Collins, Donald J., Miller, Charles F., Iii The conjugacy problem and subgroups of finite index Proc. London Math. Soc. (3) 1977 535 556

[4] Gorjaga, A. V., Kirkinskiĭ, A. S. The decidability of the conjugacy problem cannot be transferred to finite extensions of groups Algebra i Logika 1975 393 406

[5] Higman, G. Subgroups of finitely presented groups Proc. Roy. Soc. London Ser. A 1961 455 475

[6] Makanin, G. S. Equations in a free group Izv. Akad. Nauk SSSR Ser. Mat. 1982

[7] Manin, Ju. I. Vychislimoe i nevychislimoe 1980 128

[8] Miller, Charles F., Iii On group-theoretic decision problems and their classification 1971

[9] Ol′Shanskiĭ, A. Yu. On the distortion of subgroups of finitely presented groups Mat. Sb. 1997 51 98

[10] Ol′Shanskii, Alexander Yu., Sapir, Mark V. Length and area functions on groups and quasi-isometric Higman embeddings Internat. J. Algebra Comput. 2001 137 170

[11] Rotman, Joseph J. An introduction to the theory of groups 1984

[12] Valiev, M. K. On polynomial reducibility of the word problem under embedding of recursively presented groups in finitely presented groups 1975 432 438

Cité par Sources :