| Title:
|
The structure of the unit group of the group algebra $\mathbb {F}_{2^k}A_4$ (English) |
| Author:
|
Gildea, Joe |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
531-539 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The structure of the unit group of the group algebra of the group $A_4$ over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups. (English) |
| Keyword:
|
group ring |
| Keyword:
|
group algebra |
| Keyword:
|
dihedral group |
| Keyword:
|
cyclic group |
| MSC:
|
15A33 |
| MSC:
|
16S34 |
| MSC:
|
16U60 |
| MSC:
|
20C05 |
| idZBL:
|
Zbl 1237.16035 |
| idMR:
|
MR2905421 |
| DOI:
|
10.1007/s10587-011-0071-5 |
| . |
| Date available:
|
2011-06-06T10:40:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141551 |
| . |
| Reference:
|
[1] Bovdi, A. A., Erdei, L.: Unitary units in the modular group algebra of groups of order 16.Technical Reports Debrecen 96/4 (1996), 57-72. MR 1283327 |
| Reference:
|
[2] Bovdi, A. A., Szakács, A.: Unitary subgroup of the group of units of a modular group algebra of a finite abelian $p$-group.Math. Zametki 45 (1989), 23-29. MR 1019032 |
| Reference:
|
[3] Bovdi, V. A., Kovács, L. G.: Unitary units in modular group algebras.Manuscr. Math. 84 (1994), 57-72. MR 1283327, 10.1007/BF02567443 |
| Reference:
|
[4] Bovdi, V., Rosa, A. L.: On the order of the unitary subgroup of a modular group algebra.Commun. Algebra 28 (2000), 1897-1905. Zbl 0952.16022, MR 1747361, 10.1080/00927870008826934 |
| Reference:
|
[5] Creedon, L., Gildea, J.: The structure of the unit group of the group algebra ${\mathbb F}_{2^k}D_{8}$.Can. Math. Bull 54 (2011), 237-243. doi:10.4153/CMB-2010-098-5. MR 2884238, 10.4153/CMB-2010-098-5 |
| Reference:
|
[6] Creedon, L., Gildea, J.: Unitary units of the group algebra ${\mathbb F}_{2^k}Q_{8}$.Internat. J. Algebra Comput. 19 (2009), 283-286. MR 2512555, 10.1142/S0218196709005081 |
| Reference:
|
[7] Davis, P. J.: Circulant Matrices.Chelsea Publishing New York (1979). Zbl 0418.15017, MR 0543191 |
| Reference:
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[8] Hurley, T.: Group rings and rings of matrices.Int. J. Pure Appl. Math. 31 (2006), 319-335. Zbl 1136.20004, MR 2266951 |
| Reference:
|
[9] Milies, C. Polcino, Sehgal, S. K.: An Introduction to Group Rings.Kluwer Academic Publishers Dordrecht (2002). MR 1896125 |
| Reference:
|
[10] Sandling, R.: Units in the modular group algebra of a finite abelian $p$-group.J. Pure Appl. Algebra 33 (1984), 337-346. Zbl 0543.20008, MR 0761637, 10.1016/0022-4049(84)90066-5 |
| Reference:
|
[11] Sandling, R.: Presentations for units groups of modular group algebras of groups of order 16.Math. Comp. 59 (1992), 689-701. MR 1136226 |
| Reference:
|
[12] Sharma, R. K., Srivastava, J. B., Khan, M.: The unit group of $FA_4$.Publ. Math. Debrecen 71 (2007), 21-26. Zbl 1135.16033, MR 2340031 |
| . |
