Geodesic
On Canonical Generators of Subgroups
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 321-323

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

DOI

Let H be a cyclic group, K⊂H a subgroup and x, y generators of H, K. We shall say that x, y are related if y=xa where a is the index of K in H, in other words, y is the smallest positive power of x in K. The main purpose of this note is to show that for any group G one may, by means of the axiom of choice, choose for each cyclic group H⊂G a generator xH such that when K⊂H then xK , xH are related. 
Fantham, Peter. On Canonical Generators of Subgroups. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 321-323. doi: 10.4153/CMB-1971-059-4
@article{10_4153_CMB_1971_059_4,
     author = {Fantham, Peter},
     title = {On {Canonical} {Generators} of {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {321--323},
     year = {1971},
     volume = {14},
     number = {3},
     doi = {10.4153/CMB-1971-059-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-059-4/}
}
TY  - JOUR
AU  - Fantham, Peter
TI  - On Canonical Generators of Subgroups
JO  - Canadian mathematical bulletin
PY  - 1971
SP  - 321
EP  - 323
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-059-4/
DO  - 10.4153/CMB-1971-059-4
ID  - 10_4153_CMB_1971_059_4
ER  - 
%0 Journal Article
%A Fantham, Peter
%T On Canonical Generators of Subgroups
%J Canadian mathematical bulletin
%D 1971
%P 321-323
%V 14
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-059-4/
%R 10.4153/CMB-1971-059-4
%F 10_4153_CMB_1971_059_4

Cité par Sources :