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Dergiler / Journal of Algebra Combinatorics Discrete Structures and Applications / 2021 / Cilt: 8 - Sayı: 2

On unit group of finite semisimple group algebras of non-metabelian groups of order 108

Gaurav MİTTAL
Rajendra. K. SHARMA
Sayfa
59–71
Yayın Tarihi
2021-05-20
DOI
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And as a by-product obtain the unit groups.

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Amaç & Hipotez:In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$.
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Temel Bulgular & Veri:Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian.
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Sonuç & Katkı:And as a by-product obtain the unit groups.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Unit group · Finite field · Wedderburn decomposition

Abstract

In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ of non-metabelian groups of order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ groups of order $108$ but only $4$ of them are non-metabelian. We consider all the non-metabelian groups of order $108$ and find the Wedderburn decomposition of their semisimple group algebras. And as a by-product obtain the unit groups.

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Bu Makaleye Atıf Yap

MİTTAL, G., SHARMA, R. K. (2021). On unit group of finite semisimple group algebras of non-metabelian groups of order 108. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 8 - Sayı: 2, 59–71. https://ajindex.com/articles/861496

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Kaynakça (15)

  1. A. Bovdi, J. Kurdics, Lie properties of the group algebra and the nilpotency class of the group of units, J. Algebra 212 (1999) 28–64
  2. V. Bovdi, M. Salim, On the unit group of a commutative group ring, Acta Sci. Math. (Szeged) 80 (2014) 433–445
  3. R. A. Ferraz, Simple components of the center of FG/J(FG), Comm. Algebra 36 (2008) 3191–3199
  4. B. Hurley, T. Hurley, Group ring cryptography, Int. J. Pure Appl. Math. 69 (2011) 67–86
  5. P. Hurley, T. Hurley, Codes from zero-divisors and units in group rings, Int. J. Inf. Coding Theory 1 (2009) 57–87
  6. G. Karpilovsky, The Jacobson radical of group algebras, Volume 135 Elsevier (1987)
  7. M. Khan, R. K. Sharma, J. Srivastava, The unit group of FS4, Acta Math. Hungar. 118 (2008) 105-113
  8. R. Lidl, H. Niederreiter, Introduction to finite fields and their applications, Cambridge university press (1994)
  9. S. Maheshwari, R. K. Sharma, The unit group of group algebra FqSL(2;Z3), J. Algebra Comb. Discrete Appl. 3 (2016) 1–6
  10. N. Makhijani, R. K. Sharma, J. Srivastava, A note on the structure of FpkA5=J(FpkA5), Acta Sci. Math. (Szeged) 82 (2016) 29–43
  11. C. P. Milies, S. K. Sehgal, An introduction to group rings, Springer Science & Business Media (2002)
  12. G. Mittal, R. K. Sharma, On unit group of finite group algebras of non-metabelian groups up to order 72, Math Bohemica (2021
  13. G. Pazderski, The orders to which only belong metabelian groups, Math. Nachr. 95 (1980) 7–16
  14. S. Perlis, G. L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc. 68 (1950) 420–426
  15. R. K. Sharma, G. Mittal, On the unit group of a semisimple group algebra FqSL(2;Z5), Math Bohemica (2021).