Subgroups of the Adjoint Group of a Radical Ring
Canadian journal of mathematics, Tome 50 (1998) no. 1, pp. 3-15

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

It is shown that the adjoint group ${{R}^{{}^\circ }}$ of an arbitrary radical ring $R$ has a series with abelian factors and that its finite subgroups are nilpotent. Moreover, some criteria for subgroups of ${{R}^{{}^\circ }}$ to be locally nilpotent are given.
DOI : 10.4153/CJM-1998-001-9
Mots-clés : 16N20, 20F19
Amberg, B.; Dickenschied, O.; Sysak, YA. P. Subgroups of the Adjoint Group of a Radical Ring. Canadian journal of mathematics, Tome 50 (1998) no. 1, pp. 3-15. doi: 10.4153/CJM-1998-001-9
@article{10_4153_CJM_1998_001_9,
     author = {Amberg, B. and Dickenschied, O. and Sysak, YA. P.},
     title = {Subgroups of the {Adjoint} {Group} of a {Radical} {Ring}},
     journal = {Canadian journal of mathematics},
     pages = {3--15},
     year = {1998},
     volume = {50},
     number = {1},
     doi = {10.4153/CJM-1998-001-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1998-001-9/}
}
TY  - JOUR
AU  - Amberg, B.
AU  - Dickenschied, O.
AU  - Sysak, YA. P.
TI  - Subgroups of the Adjoint Group of a Radical Ring
JO  - Canadian journal of mathematics
PY  - 1998
SP  - 3
EP  - 15
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1998-001-9/
DO  - 10.4153/CJM-1998-001-9
ID  - 10_4153_CJM_1998_001_9
ER  - 
%0 Journal Article
%A Amberg, B.
%A Dickenschied, O.
%A Sysak, YA. P.
%T Subgroups of the Adjoint Group of a Radical Ring
%J Canadian journal of mathematics
%D 1998
%P 3-15
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1998-001-9/
%R 10.4153/CJM-1998-001-9
%F 10_4153_CJM_1998_001_9

[1] 1. Amberg, B. and Dickenschied, O., On the adjoint group of a radical ring. Canad.Math. Bull. (3) 38 (1995), 262–270. Google Scholar

[2] 2. Amberg, B., Franciosi, S., and de Giovanni, F., Products of groups.Oxford University Press, New York, 1992. Google Scholar

[3] 3. Amberg, B. and Ya. Sysak, P., Locally soluble products of two minimax subgroups. Proceedings of ‘Groups-Korea 1994’, W. de Gruyter, Berlin, 1995. 8–14. Google Scholar

[4] 4. Brown, K.A., The Nullstellensatz for certain group rings. J. LondonMath. Soc. (2), 26 (1982), 425–434. Google Scholar

[5] 5. Jacobson, N., Structure of Rings. Amer. Math. Soc. Colloq. Publ. 37 , 1964. Google Scholar

[6] 6. Kim, Y.K. and Rhemtulla, A.H., Weak maximality condition and polycyclic groups. Proc. Amer. Math. Soc. (3) 123 (1995), 711–714. Google Scholar

[7] 7. Kropholler, P.H., Linnel, P.A., and Moody, J.A., Applications of a new K-theoretic theorem to soluble group rings. Proc. Amer. Math. Soc. (3) 104 (1988), 675–684. Google Scholar

[8] 8. Neroslavskii, O.M., Structures that are connected with radical rings (Russian). Vesci Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk (2) 134 (1973), 5–10. Google Scholar

[9] 9. Robinson, D.J.S., Finiteness Conditions and Generalized Soluble Groups.Springer-Verlag, Berlin- Heidelberg-New York, 1972. Google Scholar

[10] 10. Rowen, L.H., Ring Theory.Academic Press, New York, 1988. Google Scholar

[11] 11. Watters, J.F., On the adjoint group of a radical ring. J. London Math. Soc. 43 (1968), 725–729. Google Scholar

[12] 12. Wehrfritz, B.A.F., Infinite Linear Groups.Springer-Verlag, Berlin, 1973. Google Scholar

[13] 13. Wilson, J.S., Two-generator conditions for residually finite groups. Bull. London Math. Soc. 23 (1991), 239–248. Google Scholar

[14] 14. Zelmanov, E., The solution of the restricted Burnside problem for groups of odd exponent. Izv. Akad. Nauk SSSR, Ser.Mat. (1) 54 (1990), 42–59. Google Scholar

[15] 15. Zelmanov, E., The solution of the restricted Burnside problem for 2-groups. Mat. Sb. (4)182 (1991), 568–592.. Google Scholar

Cité par Sources :