Geodesic
Trivial Units for Group Rings with G-adapted Coefficient Rings
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 80-89

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

For each finite group $G$ for which the integral group ring $\mathbb{Z}G$ has only trivial units, we give ring-theoretic conditions for a commutative ring $R$ under which the group ring $RG$ has nontrivial units. Several examples of rings satisfying the conditions and rings not satisfying the conditions are given. In addition, we extend a well-known result for fields by showing that if $R$ is a ring of finite characteristic and $RG$ has only trivial units, then $G$ has order at most 3.
DOI : 10.4153/CMB-2005-007-1
Mots-clés : 16S34, 16U60, 20C05 
Herman, Allen; Li, Yuanlin; Parmenter, M. M. Trivial Units for Group Rings with G-adapted Coefficient Rings. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 80-89. doi: 10.4153/CMB-2005-007-1
@article{10_4153_CMB_2005_007_1,
     author = {Herman, Allen and Li, Yuanlin and Parmenter, M. M.},
     title = {Trivial {Units} for {Group} {Rings} with {G-adapted} {Coefficient} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {80--89},
     year = {2005},
     volume = {48},
     number = {1},
     doi = {10.4153/CMB-2005-007-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/}
}
TY  - JOUR
AU  - Herman, Allen
AU  - Li, Yuanlin
AU  - Parmenter, M. M.
TI  - Trivial Units for Group Rings with G-adapted Coefficient Rings
JO  - Canadian mathematical bulletin
PY  - 2005
SP  - 80
EP  - 89
VL  - 48
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/
DO  - 10.4153/CMB-2005-007-1
ID  - 10_4153_CMB_2005_007_1
ER  - 
%0 Journal Article
%A Herman, Allen
%A Li, Yuanlin
%A Parmenter, M. M.
%T Trivial Units for Group Rings with G-adapted Coefficient Rings
%J Canadian mathematical bulletin
%D 2005
%P 80-89
%V 48
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-007-1/
%R 10.4153/CMB-2005-007-1
%F 10_4153_CMB_2005_007_1

[1] [1] Bovdi, A., The group of units of a group algebra of characteristic p. Publ. Math. Debrecen. 52(1998), 193–244. Google Scholar

[2] [2] Coleman, D. B. and Enochs, E. E., Isomorphic polynomial rings. Proc. Amer.Math. Soc. 27(1971) 247–252. Google Scholar

[3] [3] Higman, G., The units of group-rings. Proc. LondonMath. Soc. 46(1940), 231–248. Google Scholar

[4] [4] Jespers, E., Parmenter, M., and Smith, P. F., Revisiting a theorem of Higman. LondonMath. Soc. Lecture Note Ser., 211, Cambridge University Press, Cambridge, 1995, pp. 269–273. Google Scholar

[5] [5] Li, Yuanlin, The normalizer of a metabelian group in its integral group ring. J. Algebr. 256(2002), 343–351. Google Scholar

[6] [6] Passman, D. S., The Algebraic Structure of Group Rings. Wiley-Interscience, New York, 1977. Google Scholar

[7] [7] Milies, César Polcino and Sehgal, Sudarshan K., An Introduction to Group Rings. Kluwer, 2002. Google Scholar

[8] [8] Strojnowski, A., A note on u.p. groups. Comm. Algebr. 3(1980), 231–234. Google Scholar

Cité par Sources :