2016
DOI: 10.1016/j.joems.2014.08.001
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Units in finite dihedral and quaternion group algebras

Abstract: Let F q G be the group algebra of a finite group G over F q ¼ GFðqÞ. Using the Wedderburn decomposition of F 2 k D 2n =JðF 2 k D 2n Þ, we establish the structure of the unit group of F 2 k G when G is either D 4n , the dihedral group of order 4n or Q 4n , the generalized quaternion group of order 4n; n odd.

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Cited by 5 publications
(4 citation statements)
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“…The dihedral group D 12 = x, y | x 6 = y 2 = 1, yx = x 5 y . The structure of the unit group of the finite group algebra F D 12 has been studied in [9,16,25] whereas the structure of unit group of F (C 2 × D 12 ) is described in [12,18,23]. In this section, we establish the structure of the unit group of F (C n × D 12 ).…”
Section: Units Inmentioning
confidence: 99%
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“…The dihedral group D 12 = x, y | x 6 = y 2 = 1, yx = x 5 y . The structure of the unit group of the finite group algebra F D 12 has been studied in [9,16,25] whereas the structure of unit group of F (C 2 × D 12 ) is described in [12,18,23]. In this section, we establish the structure of the unit group of F (C n × D 12 ).…”
Section: Units Inmentioning
confidence: 99%
“…Let F G be the group algebra of a finite group G over a finite field F of characteristic p having q = p k elements. Let U (F G) be the unit group of F G and let J(F G) be the Jacobson radical of F G. If V = 1 + J(F G), then U (F G) ∼ = V U (F G/J(F G)) [16]. A good description of the structure of U (F G) has applications in various areas like the group ring cryptography [10] and the combinatorial number theory [5], etc.…”
Section: Introductionmentioning
confidence: 99%
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