Geodesic
A NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS
Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 137-143

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

A subgroup H of a residually finite-p group G is almost p-closed in G if H has finite p′-index in H, its closure with respect to the pro-p topology on G. We characterise polycyclic residually finite-p groups in which all subgroups are almost p-closed and discuss a few conditions that are sufficient for particular subgroups H to be almost p-closed. We also present, for each prime p, an example of a polycyclic residually-p group G for which |H: H| takes on all possible values, including infinity, as H varies.
DOI : 10.1017/S001708950999022X
Mots-clés : 20F16, 20E26 
CUTOLO, GIOVANNI; SMITH, HOWARD. A NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS. Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 137-143. doi: 10.1017/S001708950999022X
@article{10_1017_S001708950999022X,
     author = {CUTOLO, GIOVANNI and SMITH, HOWARD},
     title = {A {NOTE} {ON} {POLYCYLIC} {RESIDUALLY} {FINITE-p} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {137--143},
     year = {2010},
     volume = {52},
     number = {1},
     doi = {10.1017/S001708950999022X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950999022X/}
}
TY  - JOUR
AU  - CUTOLO, GIOVANNI
AU  - SMITH, HOWARD
TI  - A NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 137
EP  - 143
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950999022X/
DO  - 10.1017/S001708950999022X
ID  - 10_1017_S001708950999022X
ER  - 
%0 Journal Article
%A CUTOLO, GIOVANNI
%A SMITH, HOWARD
%T A NOTE ON POLYCYLIC RESIDUALLY FINITE-p GROUPS
%J Glasgow mathematical journal
%D 2010
%P 137-143
%V 52
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950999022X/
%R 10.1017/S001708950999022X
%F 10_1017_S001708950999022X

[1] 1.Passman, D. S., The algebraic structure of group rings, Pure and Applied Mathematics (Wiley-Interscience, New York, 1977). Google Scholar

[2] 2.Robinson, D. J. S., A course in the theory of groups, Second edition, Graduate Texts in Mathematics, Vol. 80 (Springer-Verlag, New York, 1996). Google Scholar | DOI

[3] 3.Roseblade, J. E., Applications of the Artin–Rees lemma to group rings, in Symposia Mathematica, Vol. XVII (Convegno sui Gruppi Infiniti, INDAM, Roma, 1973), (Academic Press, London, 1976), 471–478. Google Scholar

[4] 4.Segal, D., Polycyclic groups, Cambridge Tracts in Mathematics, Vol. 82 (Cambridge University Press, Cambridge, England, UK, 1983). Google Scholar | DOI

[5] 5.Šmel′kin, A. L., Polycyclic groups, Sibirsk. Mat. Z. 9 (1968), 234–235; English translation: Siberian Math. J., (1968), 178. Google Scholar

Cité par Sources :