Geodesic
On Weighted Geodesics in Groups
Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 86-91

Voir la notice de l'article provenant de la source Cambridge

DOI

A word W in a group G is a geodesic (weighted geodesic) if W has minimum length (minimum weight with respect to a generator weight function α) among all words equal to W. For finitely generated groups, the word problem is equivalent to the geodesic problem. We prove: (i) There exists a group G with solvable word problem, but unsolvable geodesic problem, (ii) There exists a group G with a solvable weighted geodesic problem with respect to one weight function α1, but unsolvable with respect to a second weight function α2. (iii) The (ordinary) geodesic problem and the free-product geodesic problem are independent.
DOI : 10.4153/CMB-1987-013-2
Mots-clés : 20 F 10 
Lipschutz, Seymour. On Weighted Geodesics in Groups. Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 86-91. doi: 10.4153/CMB-1987-013-2
@article{10_4153_CMB_1987_013_2,
     author = {Lipschutz, Seymour},
     title = {On {Weighted} {Geodesics} in {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {86--91},
     year = {1987},
     volume = {30},
     number = {1},
     doi = {10.4153/CMB-1987-013-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-013-2/}
}
TY  - JOUR
AU  - Lipschutz, Seymour
TI  - On Weighted Geodesics in Groups
JO  - Canadian mathematical bulletin
PY  - 1987
SP  - 86
EP  - 91
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-013-2/
DO  - 10.4153/CMB-1987-013-2
ID  - 10_4153_CMB_1987_013_2
ER  - 
%0 Journal Article
%A Lipschutz, Seymour
%T On Weighted Geodesics in Groups
%J Canadian mathematical bulletin
%D 1987
%P 86-91
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-013-2/
%R 10.4153/CMB-1987-013-2
%F 10_4153_CMB_1987_013_2

Cité par Sources :