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THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$

Year 2021, , 165 - 174, 05.01.2021
https://doi.org/10.24330/ieja.852146

Abstract

Let $F$ be a finite field of characteristic $p$.
There are three non-isomorphic non-abelian groups of order $30$.
The structure of $U(F(C_5 \times D_6))$ for $p=3$ is given in [J.
Gildea and R. Taylor, Int. Electron. J. Algebra, 24 (2018),
62-67]. In this article, we give the structure of $U(FD_{30})$ and
$U(F(C_3 \times D_{10}))$ for $p=3$.

References

  • S. F. Ansari and M. Sahai, Unit groups of group algebras of groups of order 20, Quaest. Math., to appear, https://doi.org/10.2989/16073606.2020.1727583.
  • A. Bovdi and L. Erdei, Unitary units in modular group algebras of 2-groups, Comm. Algebra, 28(2) (2000), 625-630.
  • V. Bovdi and L. G. Kovacs, Unitary units in modular group algebras, Manuscripta Math., 84(1) (1994), 57-72.
  • L. Creedon, The unit group of small group algebras and the minimum counterexample to the isomorphism problem, Int. J. Pure Appl. Math., 49(4) (2008), 531-537.
  • L. Creedon and J. Gildea, The structure of the unit group of the group algebra $F_{3^k}D_{6}$, Int. J. Pure Appl. Math., 45(2) (2008), 315-320.
  • L. Creedon and J. Gildea, The structure of the unit group of the group algebra $F_{2^k}D_{8}$, Canad. Math. Bull., 54(2) (2011), 237-243.
  • J. Gildea, The structure of the unit group of the group algebra $\Bbb F_{3^{k}}(C_3 \times D_6)$, Comm. Algebra, 38(9) (2010), 3311-3317.
  • J. Gildea, Units of the group algebra $\Bbb F_{5^k}(C_{5} \rtimes C_4)$, Int. Electron. J. Algebra, 9 (2011), 220-227.
  • J. Gildea and R. Taylor, Units of the group algebra of the group $C_n \times D_6$ over any finite field of characteristic 3, Int. Electron. J. Algebra, 24 (2018), 62-67.
  • K. Kaur and M. Khan, Units in $F_2D_{2p}$, J. Algebra Appl., 13(2) (2014), 1350090 (9 pp).
  • M. Khan, Structure of the unit group of $FD_{10}$, Serdica Math. J., 35(1) (2009), 15-24.
  • Y. Kumar, R. K. Sharma and J. B. Srivastava, The structure of the unit group of the group algebra $\Bbb FS_5$ where $\Bbb F$ is a finite field with char$(\Bbb F)=p>5$, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 33(2) (2017), 187-191.
  • N. Makhijani, R. K. Sharma and J. B. Srivastava, Units in $\Bbb F_{2^k}D_{2n}$, Int. J. Group Theory, 3(3) (2014), 25-34.
  • N. Makhijani, R. K. Sharma and J. B. Srivastava, The unit group of $\Bbb F_{q}[D_{30}]$, Serdica Math. J., 41(2-3) (2015), 185-198.
  • 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.
  • Z. Raza and M. Ahmad, On the structure of the unitary subgroup of the group algebra $\Bbb F_{2^q}D_{2^n}$, J. Algebra Appl., 13(4) (2014), 1350139 (8 pp).
  • Z. Raza and M. Ahmad, Structure of the unitary subgroup of the group algebra $\Bbb F_{2^n}(QD)_{16}$, J. Algebra Appl., 17(4) (2018), 1850060 (7 pp).
  • M. Sahai and S. F. Ansari, Unit groups of the finite group algebras of generalized quaternion groups, J. Algebra Appl., 19(6) (2020), 2050112 (5 pp).
  • R. Sandling, Units in the modular group algebra of a finite abelian $p$-group, J. Pure Appl. Algebra, 33(3) (1984), 337-346.
  • G. Tang and G. Yanyan, The unit groups of $FG$ of groups 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(1) (2014), 149-157.
Year 2021, , 165 - 174, 05.01.2021
https://doi.org/10.24330/ieja.852146

Abstract

References

  • S. F. Ansari and M. Sahai, Unit groups of group algebras of groups of order 20, Quaest. Math., to appear, https://doi.org/10.2989/16073606.2020.1727583.
  • A. Bovdi and L. Erdei, Unitary units in modular group algebras of 2-groups, Comm. Algebra, 28(2) (2000), 625-630.
  • V. Bovdi and L. G. Kovacs, Unitary units in modular group algebras, Manuscripta Math., 84(1) (1994), 57-72.
  • L. Creedon, The unit group of small group algebras and the minimum counterexample to the isomorphism problem, Int. J. Pure Appl. Math., 49(4) (2008), 531-537.
  • L. Creedon and J. Gildea, The structure of the unit group of the group algebra $F_{3^k}D_{6}$, Int. J. Pure Appl. Math., 45(2) (2008), 315-320.
  • L. Creedon and J. Gildea, The structure of the unit group of the group algebra $F_{2^k}D_{8}$, Canad. Math. Bull., 54(2) (2011), 237-243.
  • J. Gildea, The structure of the unit group of the group algebra $\Bbb F_{3^{k}}(C_3 \times D_6)$, Comm. Algebra, 38(9) (2010), 3311-3317.
  • J. Gildea, Units of the group algebra $\Bbb F_{5^k}(C_{5} \rtimes C_4)$, Int. Electron. J. Algebra, 9 (2011), 220-227.
  • J. Gildea and R. Taylor, Units of the group algebra of the group $C_n \times D_6$ over any finite field of characteristic 3, Int. Electron. J. Algebra, 24 (2018), 62-67.
  • K. Kaur and M. Khan, Units in $F_2D_{2p}$, J. Algebra Appl., 13(2) (2014), 1350090 (9 pp).
  • M. Khan, Structure of the unit group of $FD_{10}$, Serdica Math. J., 35(1) (2009), 15-24.
  • Y. Kumar, R. K. Sharma and J. B. Srivastava, The structure of the unit group of the group algebra $\Bbb FS_5$ where $\Bbb F$ is a finite field with char$(\Bbb F)=p>5$, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 33(2) (2017), 187-191.
  • N. Makhijani, R. K. Sharma and J. B. Srivastava, Units in $\Bbb F_{2^k}D_{2n}$, Int. J. Group Theory, 3(3) (2014), 25-34.
  • N. Makhijani, R. K. Sharma and J. B. Srivastava, The unit group of $\Bbb F_{q}[D_{30}]$, Serdica Math. J., 41(2-3) (2015), 185-198.
  • 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.
  • Z. Raza and M. Ahmad, On the structure of the unitary subgroup of the group algebra $\Bbb F_{2^q}D_{2^n}$, J. Algebra Appl., 13(4) (2014), 1350139 (8 pp).
  • Z. Raza and M. Ahmad, Structure of the unitary subgroup of the group algebra $\Bbb F_{2^n}(QD)_{16}$, J. Algebra Appl., 17(4) (2018), 1850060 (7 pp).
  • M. Sahai and S. F. Ansari, Unit groups of the finite group algebras of generalized quaternion groups, J. Algebra Appl., 19(6) (2020), 2050112 (5 pp).
  • R. Sandling, Units in the modular group algebra of a finite abelian $p$-group, J. Pure Appl. Algebra, 33(3) (1984), 337-346.
  • G. Tang and G. Yanyan, The unit groups of $FG$ of groups 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(1) (2014), 149-157.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Meena Sahaı This is me

Sheere Farhat Ansarı This is me

Publication Date January 5, 2021
Published in Issue Year 2021

Cite

APA Sahaı, M., & Ansarı, S. F. (2021). THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$. International Electronic Journal of Algebra, 29(29), 165-174. https://doi.org/10.24330/ieja.852146
AMA Sahaı M, Ansarı SF. THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$. IEJA. January 2021;29(29):165-174. doi:10.24330/ieja.852146
Chicago Sahaı, Meena, and Sheere Farhat Ansarı. “THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$”. International Electronic Journal of Algebra 29, no. 29 (January 2021): 165-74. https://doi.org/10.24330/ieja.852146.
EndNote Sahaı M, Ansarı SF (January 1, 2021) THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$. International Electronic Journal of Algebra 29 29 165–174.
IEEE M. Sahaı and S. F. Ansarı, “THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$”, IEJA, vol. 29, no. 29, pp. 165–174, 2021, doi: 10.24330/ieja.852146.
ISNAD Sahaı, Meena - Ansarı, Sheere Farhat. “THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$”. International Electronic Journal of Algebra 29/29 (January 2021), 165-174. https://doi.org/10.24330/ieja.852146.
JAMA Sahaı M, Ansarı SF. THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$. IEJA. 2021;29:165–174.
MLA Sahaı, Meena and Sheere Farhat Ansarı. “THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$”. International Electronic Journal of Algebra, vol. 29, no. 29, 2021, pp. 165-74, doi:10.24330/ieja.852146.
Vancouver Sahaı M, Ansarı SF. THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$. IEJA. 2021;29(29):165-74.