Geodesic
Algebraic conjugacy of irreducible characters of a group $GL(2,8)$
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 129-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The structure of the tables of characters for groups $GL(2,q)$ is known for a long time. However, with setting a specific value for $q$, its finding in explicit form can be very difficult because even calculating numbers, which determine the position of characters in the table, requires considerable effort. It also turns out that specific values of some characters can't be easy for calculating because of nontrivial relations between roots of $1$ of various degrees. In the work a table of the characters of the group $GL(2,8)$, construction of which demonstrated the difficulties above, is presented explicitly. In particular, there are discovered interesting connections between the roots of $1$ degree $21$. Algebraic conjugacy of the characters of the group $GL(2,8)$ is fully defined, which allowed to calculate the rank of the group of central units of the integral group ring of this group.
Keywords: character, table of characters, group ring, central unit of the group ring, rank of the group of central units. 
@article{CHFMJ_2019_4_2_a0,
     author = {R. Zh. Aleev and O. V. Mitina and A. D. Godova},
     title = {Algebraic conjugacy of irreducible characters of a group $GL(2,8)$},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {129--141},
     year = {2019},
     volume = {4},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a0/}
}
TY  - JOUR
AU  - R. Zh. Aleev
AU  - O. V. Mitina
AU  - A. D. Godova
TI  - Algebraic conjugacy of irreducible characters of a group $GL(2,8)$
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2019
SP  - 129
EP  - 141
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a0/
LA  - ru
ID  - CHFMJ_2019_4_2_a0
ER  - 
%0 Journal Article
%A R. Zh. Aleev
%A O. V. Mitina
%A A. D. Godova
%T Algebraic conjugacy of irreducible characters of a group $GL(2,8)$
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2019
%P 129-141
%V 4
%N 2
%U http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a0/
%G ru
%F CHFMJ_2019_4_2_a0
R. Zh. Aleev; O. V. Mitina; A. D. Godova. Algebraic conjugacy of irreducible characters of a group $GL(2,8)$. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 129-141. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a0/

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

[2] Aleev R.Zh., Ismagilova E.F., Karlina N.G., “Central units of an integral group ring of the group $GL_2(5)$”, Algebra and linear optimization, Ural Branch of Russian Academy of Sciences, Yekaterinburg, 2002, 12–14 (In Russ.)

[3] R. Zh. Aleev, O. V. Mitina, A. P. Mitin, “Central unit group of integral group ring of GL(2,4)”, Abstracts of the International Conference and PhD Summer School, Ural Branch of Russian Academy of Sciences, Yekaterinburg, 2015, 32 | MR

[4] Belonogov V.A., “On small interactions in finite groups”, Proceedings of Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, 2, 1992, 3–18 (In Russ.) | MR | Zbl

[5] Van der Varden B.L., Algebra, 2nd ed., Nauka Publ., Moscow, 1979, 624 pp. (In Russ.) | MR

[6] Aleev R.Zh., “Central elements of integral group rings”, Algebra and Logic, 39:5 (2000), 293–300 | MR | Zbl

[7] Aleev R.Ž., Tsybina N.A., “Computing ranks of groups of central units of integral group rings of finite groups”, Bulletin of South Urala State University. Series: Computational mathematics and informatics, 4:1 (2015), 71–85 (In Russ.)