Geodesic
On the Wielandt subgroup of infinite soluble groups
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 121-125

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

The Wielandt subgroup w(G) of a group G is defined to be the intersection of the normalizers of all the subnormal subgroups of G. If G is a group satisfying the minimal condition on subnormal subgroups then Wielandt [10] showed that w(G) contains every minimal normal subgroup of G, and so contains the socle of G, and, later, Robinson [6] and Roseblade [9] proved that w(G) has finite index in G. 
Brandl, Rolf; Franciosi, Silvana; Giovanni, Francesco de. On the Wielandt subgroup of infinite soluble groups. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 121-125. doi: 10.1017/S0017089500009149
@article{10_1017_S0017089500009149,
     author = {Brandl, Rolf and Franciosi, Silvana and Giovanni, Francesco de},
     title = {On the {Wielandt} subgroup of infinite soluble groups},
     journal = {Glasgow mathematical journal},
     pages = {121--125},
     year = {1990},
     volume = {32},
     number = {2},
     doi = {10.1017/S0017089500009149},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009149/}
}
TY  - JOUR
AU  - Brandl, Rolf
AU  - Franciosi, Silvana
AU  - Giovanni, Francesco de
TI  - On the Wielandt subgroup of infinite soluble groups
JO  - Glasgow mathematical journal
PY  - 1990
SP  - 121
EP  - 125
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009149/
DO  - 10.1017/S0017089500009149
ID  - 10_1017_S0017089500009149
ER  - 
%0 Journal Article
%A Brandl, Rolf
%A Franciosi, Silvana
%A Giovanni, Francesco de
%T On the Wielandt subgroup of infinite soluble groups
%J Glasgow mathematical journal
%D 1990
%P 121-125
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009149/
%R 10.1017/S0017089500009149
%F 10_1017_S0017089500009149

[1] 1.Baer, R., Kern, Der, eine charakteristische Untergruppe, Compositio Math. 1 (1934), 254–283. Google Scholar

[2] 2.Cooper, C. D. H., Power automorphisms of a group, Math. Z. 107 (1968), 335–356. Google Scholar | DOI

[3] 3.Cossey, J., The Wielandt subgroup of a polycyclic group, Australian National University, Math. Research Report Series 19 (1988). Google Scholar

[4] 4.Hall, P., On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595–622. Google Scholar | DOI

[5] 5.Robinson, D. J. S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc. 60 (1964), 21–38. Google Scholar | DOI

[6] 6.Robinson, D. J. S., On the theory of subnormal subgroups, Math. Z. 89 (1965), 30–51. Google Scholar | DOI

[7] 7.Robinson, D. J. S., A note on groups of finite rank, Compositio Math. 21 (1969), 240–246. Google Scholar

[8] 8.Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Springer, 1972). Google Scholar | DOI

[9] 9.Roseblade, J. E., On certain subnormal coalition classes, J. Algebra 1 (1964), 132–138. Google Scholar | DOI

[10] 10.Wielandt, H., Uber den Normalisator der subnormalen Untergruppen, Math. Z. 69 (1958), 463–465. Google Scholar | DOI

Cité par Sources :