The group of units of group algebras of abelian groups of order 36 and $C_{3}\times A_{4}$ over any finite field
The group of units of group algebras of abelian groups of order 36 and $C_{3}\times A_{4}$ over any finite field
Let $\mathcal{FG}$ be the group algebra of the group $\mathcal{G}$ over the field $\mathcal{F}$ having characteristic $p>0$ and $q=p^{n}$ elements and $\mathscr{U}\mathcal{(FG)}$ be the unit group of $\mathcal{FG}$. In this paper, we are proceeding to determine the structure of unit group of group algebra of all four non isomorphic abelian groups and one non abelian group $C_{3}\times A_{4}$ of order $36$, for any prime $p>0$.
Keywords:
Group algebras unit groups, jacobson radical,
___
- S. F. Ansari and M. Sahai, Unit groups of group algebras of groups of order 20, Quaest. Math., 44(4) (2021), 503-511.
- S. Bhatt and H. Chandra, Structure of unit group of $F_{p^n}D_{60}$, Asian-Eur. J. Math., 14(5) (2021), 2150075 (9 pp.).
- A. A. Bovdi and A. Szakact, A basis for the unitary subgroup of the group of units in a finite commutative group algebra, Publ. Math. Debrecen, 46(1-2) (1995), 97-120.
- R. A. Ferraz, Simple components of the center of FG/J(FG), Comm. Algebra, 36(9) (2008), 3191-3199.
- J. Gildea, The structure of the unitary units of the group algebra $F_{2^k} D_8$, Int. Electron. J. Algebra, 9 (2011), 171-176.
- J. Gildea and F. Monaghan, Units of some group algebras of groups of order 12 over any finite field of characteristic 3, Algebra Discrete Math., 11(1) (2011), 46-58.
- G. Higman, Units in Group Rings, Ph.D. Thesis, Univ. Oxford, 1940.
- G. Higman, The units of group rings, Proc. London Math. Soc., (2)46 (1940), 231-248.
- S. A. Jennings, The structure of the group ring of a p-group over a modular fields, Trans. Amer. Math.Soc., 50(1) (1941), 175-185.
- G. Karpilovsky, Unit Groups of Classical Rings, The Clarendon Press, Oxford University Press, New York, 1988.
- G. Karplipovsky, The Jacobson Radical of Group Algebras, North-Holland Publishing Co., Amsterdam, 1987.
- M. Khan, R. K. Sharma and J. B. Srivastava, The unit group of $FS_{4}$, Acta Math. Hungar., 118(1-2) (2008), 105-113.
- C. P. Milies and S. K. Sehgal, An Introduction to Group Rings Algebras and Applications, Springer Science & Business Media, 2002.
- F. Monaghan, Units of some group algebras of non-abelian groups of order 24 over any finite field of characteristic 3, Int. Electron. J. Algebra, 12 (2012), 133-161.
- D. S. Passman, The Algebraic Structure of Group Rings, Pure and Applied Mathematics, Wiley, New York, 1977.
- M. Sahai and S. F. Ansari, Unit groups of finite group algebras of abelian groups of order at most 16, Asian-Eur. J. Math., 14(3) (2021), 2150030 (17 pp.).
- R. K. Sharma, J. B. Srivastava and M. Khan, The unit group of $FS_3$, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 23(2) (2007), 129-142.
- R. K. Sharma, J. B. Srivastava and M. Khan, The unit group of $FA_4$, Publ. Math. Debrecen, 71(1-2) (2007), 21-26.
- G. Tang and Y. Gao, The unit group of FG of group with order 12, Int. J. Pure Appl. Math., 73(2) (2011), 143-158.
- G. Tang, Y. Wei and Y. Li, Unit groups of group algebras of some small groups, Czechoslovak Math. J., 64(139)(1) (2014), 149-157.
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI