Unit groups of group algebras of certain dihedral groups-II

Sahai, Meena; Ansari, Sheere Farhat

doi:10.1142/s1793557119500669

Cited by 9 publications

(3 citation statements)

References 3 publications

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“…The current research has renew focused on factoring nonabelian groups into subsets (see [1,11]). The study by Sahai and Ansari [13] adds to the growing body of research in this area and provides insights into the properties of non-abelian groups and how they can be factored.…”

Section: Introductionmentioning

confidence: 99%

The Exhaustion Numbers of the Generalized Quaternion Groups

Chen¹,

Sin²

2023

MJMS

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Let G be a finite group and let T be a non-empty subset of G. For any positive integer k, let Tk={t1…tk∣t1,…,tk∈T}. The set T is called exhaustive if Tn=G for some positive integer n where the smallest positive integer n, if it exists, such that Tn=G is called the exhaustion number of T and is denoted by e(T). If Tk≠G for any positive integer k, then T is a non-exhaustive subset and we write e(T)=∞. In this paper, we investigate the exhaustion numbers of subsets of the generalized quaternion group Q2n=⟨x, y∣x2n−1=1, x2n−2=y2, yx=x2n−1−1y⟩ where n≥3. We show that Q2n has no exhaustive subsets of size 2 and that the smallest positive integer k such that any subset T⊆Q2n of size greater than or equal to k is exhaustive is 2n−1+1. We also show that for any integer k∈{3,…,2n}, there exists an exhaustive subset T of Q2n such that |T|=k .

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Section: Introductionmentioning

confidence: 99%

The Exhaustion Numbers of the Generalized Quaternion Groups

Chen¹,

Sin²

2023

MJMS

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“…The structures of U (F S 4 ) and U (F SL(2, Z 3 )) are given in [3,4], respectively. Also, the structure of U (F D 24 ) for p ≤ 3 is given in [4,7] and for p > 3 in [8]. For p = 2, Maheshwari [4], obtained the structure of U (F G), where G is a non-abelian group of order 24.…”

Section: Introductionmentioning

confidence: 99%

“…

Let F be a finite field of characteristic p. The structures of the unit groups of group algebras over F of the three groups D24, S4 and SL(2, Z3) of order 24 are completely described in [3,4,5,7,8]. In this paper, we give the unit groups of the group algebras over F of the remaining groups of order 24,

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confidence: 99%