Units in finite dihedral and quaternion group algebras
Let FqG be the group algebra of a finite group G over Fq=GF(q). Using the Wedderburn decomposition of F2kD2n/J(F2kD2n), we establish the structure of the unit group of F2kG when G is either D4n, the dihedral group of order 4n or Q4n, the generalized quaternion group of order 4n,n odd.
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| Language: | English |
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SpringerOpen
2016-01-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X14001023 |
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doaj-cb14f3b738784185808d6527f891c3132020-11-25T01:37:52ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2016-01-012415710.1016/j.joems.2014.08.001Units in finite dihedral and quaternion group algebrasNeha MakhijaniR.K. SharmaJ.B. SrivastavaLet FqG be the group algebra of a finite group G over Fq=GF(q). Using the Wedderburn decomposition of F2kD2n/J(F2kD2n), we establish the structure of the unit group of F2kG when G is either D4n, the dihedral group of order 4n or Q4n, the generalized quaternion group of order 4n,n odd.http://www.sciencedirect.com/science/article/pii/S1110256X14001023Group algebraUnit groupWedderburn decompositionJacobson radical |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Neha Makhijani R.K. Sharma J.B. Srivastava |
| spellingShingle |
Neha Makhijani R.K. Sharma J.B. Srivastava Units in finite dihedral and quaternion group algebras Journal of the Egyptian Mathematical Society Group algebra Unit group Wedderburn decomposition Jacobson radical |
| author_facet |
Neha Makhijani R.K. Sharma J.B. Srivastava |
| author_sort |
Neha Makhijani |
| title |
Units in finite dihedral and quaternion group algebras |
| title_short |
Units in finite dihedral and quaternion group algebras |
| title_full |
Units in finite dihedral and quaternion group algebras |
| title_fullStr |
Units in finite dihedral and quaternion group algebras |
| title_full_unstemmed |
Units in finite dihedral and quaternion group algebras |
| title_sort |
units in finite dihedral and quaternion group algebras |
| publisher |
SpringerOpen |
| series |
Journal of the Egyptian Mathematical Society |
| issn |
1110-256X |
| publishDate |
2016-01-01 |
| description |
Let FqG be the group algebra of a finite group G over Fq=GF(q). Using the Wedderburn decomposition of F2kD2n/J(F2kD2n), we establish the structure of the unit group of F2kG when G is either D4n, the dihedral group of order 4n or Q4n, the generalized quaternion group of order 4n,n odd. |
| topic |
Group algebra Unit group Wedderburn decomposition Jacobson radical |
| url |
http://www.sciencedirect.com/science/article/pii/S1110256X14001023 |
| work_keys_str_mv |
AT nehamakhijani unitsinfinitedihedralandquaterniongroupalgebras AT rksharma unitsinfinitedihedralandquaterniongroupalgebras AT jbsrivastava unitsinfinitedihedralandquaterniongroupalgebras |
| _version_ |
1725056818213814272 |