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.

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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
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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