Unitary subgroup of the multiplicative group of a modular group algebra of a finite abelian p-group

Bovdi, A. A.; Sakach, A. A.

doi:10.1007/bf01158231

Cited by 19 publications

(22 citation statements)

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“…The structure of Ã-unitary subgroup of V ðF 2 CÞ was described in Bovdi-Sakach (1989, 1995. According to these results the order of V Ã ðF 2 CÞ is…”

Section: Reprintsmentioning

confidence: 99%

On Units of Group Algebras of 2-Groups of Maximal Class

Balogh

Bovdi

2004

Communications in Algebra

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Abstract. We determine the number of elements of order two in the group of normalized units V (F 2 G) of the group algebra F 2 G of a 2-group of maximal class over the field F 2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V (F 2 G) and V (F 2 H) are isomorphic if and only if G and H are isomorphic. Notation and results.Let G be a finite p-group and F p G its group algebra over the fieldis called the group of normalized units. Evidently V (F p G) is a p-group and its order is p |G|−1 .Let C = a | a 2 n = 1 be the cyclic group of order 2 n , where n ≥ 2. Consider the following extensions of C:which are the generalized quaternion group, the dihedral group and the semidihedral group respectively. It is well-known that a finite 2-group of maximal class coincides with one of these groups.

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“…The structure of Ã-unitary subgroup of V ðF 2 CÞ was described in Bovdi-Sakach (1989, 1995. According to these results the order of V Ã ðF 2 CÞ is…”

Section: Reprintsmentioning

confidence: 99%

On Units of Group Algebras of 2-Groups of Maximal Class

Balogh

Bovdi

2004

Communications in Algebra

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“…Bovdi and Szakacs in [3] gave the basis for V * (FG), where characteristic of F is greater than 2. The structure of V * (F 2 G) for all groups of order 8 and 16 is given by Bovdi and Erdei [2].…”

Section: Introductionmentioning

confidence: 99%

On the unitary units of the group algebra 𝔽_2^kQ₁₆

Raza

Ali

2015

Asian-European J. Math.

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In this note, the structure of unitary unit groups V * (F 2 k Q 16 ) is investigated, where Q 16 , is quaternion group of order 16, and F 2 k is any finite field of characteristic 2, with 2 k elements. In particular, we give the center Z(V * (F 2 k Q 16 )) of unitary units subgroup V * (F 2 k Q 16 ) of group algebra F 2 k Q 16 . The structure of the unitary unit subgroup V * (F 2 k Q 16 ) is described with the help of the Z(V * (F 2 k Q 16 )).

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“…Bovdi and Szakacs [6] have given the basis for V * (FG), where characteristic of F is greater than 2. The structure of V * (F 2 G) for all groups of order 8 and 16 is given by Bovdi and Erdei [2].…”

Section: Introductionmentioning

confidence: 99%