Geodesic
Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 622-639 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe groups of central units of integral group rings of Frobenius metacyclic groups of orders 39 and 156, and thus complete the study on groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups for the case when $m$ is a prime number.
Keywords: metacyclic group, central units, integral group rings.
Mots-clés : Frobenius group 
@article{SEMR_2021_18_1_a8,
     author = {E. O. Shumakova},
     title = {Groups of central units of rank 1 of integral group rings of {Frobenius} metacyclic groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {622--639},
     year = {2021},
     volume = {18},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a8/}
}
TY  - JOUR
AU  - E. O. Shumakova
TI  - Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 622
EP  - 639
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a8/
LA  - en
ID  - SEMR_2021_18_1_a8
ER  - 
%0 Journal Article
%A E. O. Shumakova
%T Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 622-639
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a8/
%G en
%F SEMR_2021_18_1_a8
E. O. Shumakova. Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 622-639. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a8/

[1] K. Ireland, M. Rosen, A Classical introduction to modern number theory, Mir, M., 1987 | MR | Zbl

[2] R.Ž. Aleev, Central units of integral group rings of finite cyclic groups, dissertation for the degree of doctor of physical and mathematical sciences, Chelyabinsk State University, Chelyabinsk, 2000 | MR

[3] R.Ž. Aleev, A.N. Vorob'ev, E.A. Ketova, E.O. Shumakova, “Units of integral group rings of cyclic 3-groups”, International conference “Mal'tsev readings”, thesis of reports (Novosibirsk, 2018), 71

[4] R.Ž. Aleev, O.V. Mitina, T.A. Khanenko, “Local units of integral group ring of cyclic group of order 64 for character with character field $Q_{64}$”, Chelyabinsk Physical and Mathematical Journal, 3:3 (2018), 253–275 | MR | Zbl

[5] R.Ž. Aleev, O.V. Mitina, T.A. Khanenko, “Finding of units for integral group rings of orders 16 and 32 cyclic groups”, Chelyabinsk Physical and Mathematical Journal, 1:4 (2016), 30–55 | MR | Zbl

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

[7] V.A. Belonogov, Representations and characters in the theory of finite groups, Ural'skoe Otdelenie AN SSSR, Sverdlovsk, 1990 | MR | Zbl

[8] Z.I. Borevich, I.R. Shafarevich, Number theory, Nauka, M., 1985 | MR | Zbl

[9] B.L. Van der Waerden, Algebra, Nauka, M., 1979 | MR | Zbl

[10] Ch. Curtis, I. Reiner, Representation theory of finite groups and associative algebras, John Wiley Sons, New York-London | MR | Zbl

[11] E.O. Shumakova, “Central units in integral group rings for Frobenius metacyclic groups”, Sib. Électron. Mat. Izv., 5 (2008), 691–698 | MR | Zbl

[12] E.O. Shumakova, “A description of the group of central unitsin integral group rings of Frobenius groups”, Innovation in science, 7 (2016), 60–65

[13] E.O. Shumakova, Groups of central units of integral group rings of finite solvable groups, dissertation for the degree of candidate of physical and mathematical sciences, Chelyabinsk State University, Chelyabinsk, 2009 | MR