Geodesic
The decomposition theorem and ranks of central unit groups of integer group rings of groups $PGL_2(q)$, $q$ odd
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 652-672.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study central unit groups of integer group rings of groups $PGL_2(q)$, $q$ odd, prove the decomposition theorem, and find the ranks of those groups.
Keywords: group characters, central units, group rings. 
@article{SEMR_2008_5_a29,
     author = {R. Zh. Aleev and O. V. Mitina},
     title = {The decomposition theorem and ranks of central unit groups of integer group rings of groups  $PGL_2(q)$, $q$ odd},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {652--672},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a29/}
}
TY  - JOUR
AU  - R. Zh. Aleev
AU  - O. V. Mitina
TI  - The decomposition theorem and ranks of central unit groups of integer group rings of groups  $PGL_2(q)$, $q$ odd
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2008
SP  - 652
EP  - 672
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2008_5_a29/
LA  - ru
ID  - SEMR_2008_5_a29
ER  - 
%0 Journal Article
%A R. Zh. Aleev
%A O. V. Mitina
%T The decomposition theorem and ranks of central unit groups of integer group rings of groups  $PGL_2(q)$, $q$ odd
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2008
%P 652-672
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2008_5_a29/
%G ru
%F SEMR_2008_5_a29
R. Zh. Aleev; O. V. Mitina. The decomposition theorem and ranks of central unit groups of integer group rings of groups  $PGL_2(q)$, $q$ odd. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 652-672. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a29/

[1] Aleev R. Zh., Mitina O. V., Teoriya tsentralnykh edinits tselochislennykh gruppovykh kolets grupp $PSL_2(q)$, $q$ nechetno, Dep. VINITI 1462-V2005, 11.11.05, Red. Chelyab. gos. un-ta, 63 pp.

[2] Aleev R. Zh., Peravina O. V., “Rangi grupp tsentralnykh edinits tselochislennykh gruppovykh kolets grupp $PSL(2,q)$, $q$ nechetno”, Vestnik Chelyab. GU, seriya “Matematika. Mekhanika”, 1(4) (1999), 5–15

[3] Belonogov V. A., Predstavleniya i kharaktery v teorii konechnykh grupp, Sverdlovsk, 1990, 378 pp. | MR

[4] Belonogov V. A., “O malykh vzaimodeistviyakh v konechnykh gruppakh”, Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 2, 1992, 3–18 | Zbl

[5] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, Glavn. red. fiz.-mat. lit., M., 1985, 504 pp. | MR | Zbl

[6] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, Glavn. red. fiz.-mat. lit., M., 1969, 668 pp. | MR

[7] Aleev R. Ž., “Higman's central unit theory, units of integral group rings of finite cyclic groups and Fibonacci numbers”, Intern. J. Algebra and Computations, 4:3 (1994), 309–358 | DOI | MR | Zbl

[8] Li Y., Parmenter M. M., “Central units of the integral group ring $\mathbb ZA5$”, Proc. Amer. Math. Soc., 25:1 (1997), 61–65 | MR

[9] Higman G., “The units of group rings”, Proc. London Math. Soc., 46 (1940), 231–248 | DOI | MR