R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Finding of units for integer group rings of orders 16 and 32 cyclic groups”, Chelyab. Fiz.-Mat. Zh., 1:4 (2016), 30

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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2016, Volume 1, Issue 4, Pages 30–55 (Mi chfmj35)

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Finding of units for integer group rings of orders 16 and 32 cyclic groups

R. Zh. Aleev^ab, O. V. Mitina^ab, T. A. Khanenko^a

^a Chelyabinsk State University, Chelyabinsk, Russia
^b South Ural State University (National Research University), Chelyabinsk, Russia

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Abstract: The groups of integer group rings units for cyclic groups of orders 16 and 32 are described. This description is obtained as a direct product of their subgroups. Generators of one of the subgroups are found for orders 16 and 32.

Keywords: group ring, group ring unit, cyclic group, primitive root, track, character.

Received: 21.10.2016
Revised: 07.11.2016

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

Citation: R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Finding of units for integer group rings of orders 16 and 32 cyclic groups”, Chelyab. Fiz.-Mat. Zh., 1:4 (2016), 30–55

Citation in format AMSBIB

\Bibitem{AleMitKha16}

\by R.~Zh.~Aleev, O.~V.~Mitina, T.~A.~Khanenko

\paper Finding of units  for integer group rings of orders 16 and 32 cyclic groups

\jour Chelyab. Fiz.-Mat. Zh.

\yr 2016

\vol 1

\issue 4

\pages 30--55

\mathnet{http://mi.mathnet.ru/chfmj35}

\elib{https://elibrary.ru/item.asp?id=27664291}

Linking options:

https://www.mathnet.ru/eng/chfmj35

https://www.mathnet.ru/eng/chfmj/v1/i4/p30

This publication is cited in the following 3 articles:

E. O. Shumakova, “Groups of central units of rank 1 of integral group rings of Frobenius metacyclic groups”, Sib. elektron. matem. izv., 18:1 (2021), 622–639
R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Lokalnye edinitsy tselochislennogo gruppovogo koltsa tsiklicheskoi gruppy poryadka 64 dlya kharaktera s polem kharaktera ${\mathbb Q}_{64}$ ”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 253–275
R. Zh. Aleev, O. V. Mitina, T. A. Khanenko, “Opisanie gruppy edinits tselochislennogo gruppovogo koltsa tsiklicheskoi gruppy poryadka $16$ ”, Tr. IMM UrO RAN, 23, no. 4, 2017, 32–42

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Chelyabinskiy Fiziko-Matematicheskiy Zhurnal

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