Results 251 to 260 of about 3,661,637 (292)
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Units of Group Algebras of the Fours Group
Bulletin of the Iranian Mathematical Society, 2019In this paper, the (Passman) fours group \(\Gamma \) is defined in the following way: \[\Gamma = \langle x,y \vert (x^2)^y = x^{-2}, (y^2)^x = y^{-2}\rangle.\] Let \(K \Gamma\) be the group algebra of the group \(\Gamma\) over a field \(K\). The authors introduce the definition of \(L\)-length in the group algebra \(K \Gamma\).
Abdollahi, Alireza +1 more
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1999
For a commutative ring R with identity and an arbitrary group G, let RG denote the group ring of G over R and U(RG) its group of units. It is of interest, see the survey by Dennis (1977), to determine the necessary and sufficient conditions on R and G in order that U(RG) has a specific group-theoretic property, e.g., solvability, nilpotence, etc ...
Ashwani K. Bhandari, I. B. S. Passi
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For a commutative ring R with identity and an arbitrary group G, let RG denote the group ring of G over R and U(RG) its group of units. It is of interest, see the survey by Dennis (1977), to determine the necessary and sufficient conditions on R and G in order that U(RG) has a specific group-theoretic property, e.g., solvability, nilpotence, etc ...
Ashwani K. Bhandari, I. B. S. Passi
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Unit groups of group algebras of certain dihedral groups-II
Asian-European Journal of Mathematics, 2019In this paper, we establish the structure of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text] is a finite field and [Formula: see text] is the dihedral group of order [Formula: see text].
Meena Sahai, Sheere Farhat Ansari
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Unit groups of group algebras of groups of order 18
Communications in Algebra, 2021There are five non-isomorphic groups of order 18. Of these two groups are abelian and the rest are non-abelian.
Meena Sahai, Sheere Farhat Ansari
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Units in Group Algebras of Finite p-Groups
Journal of Mathematical Sciences, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bovdi, Adalbert, Patay, Zoltán
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Canadian Mathematical Bulletin, 1980
If R is a ring such that x, y ∈ R and xy = 0 imply yx = 0 and G≠ 1, an ordered group, then we show that ∑ αgg is a unit in RG if and only if there exists ∑ βhh in RG such that ∑ αgβg-1 = 1 and αgβh is nilpotent whenever gh≠l. We also show that if R is a ring with no nilpotent elements ≠ 0 and no idempotents ≠ 0, 1 then RG has only trivial units.
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If R is a ring such that x, y ∈ R and xy = 0 imply yx = 0 and G≠ 1, an ordered group, then we show that ∑ αgg is a unit in RG if and only if there exists ∑ βhh in RG such that ∑ αgβg-1 = 1 and αgβh is nilpotent whenever gh≠l. We also show that if R is a ring with no nilpotent elements ≠ 0 and no idempotents ≠ 0, 1 then RG has only trivial units.
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Cyclotomic units and the unit group of an elementary abelian group ring
Archiv der Mathematik, 1985Let A be a finite abelian group, and let U(A) be the group of units of \({\mathbb{Z}}A\) modulo torsion. Consider the maps \[ \prod_{C}U(C)\to^{\alpha}U(A)\to^{\beta}\prod_{K}U(K) \] where C and K run over the sets of cyclic subgroups and factor-groups of A, respectively.
Hoechsmann, K., Sehgal, S. K., Weiss, A.
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Unit groups of group algebras of groups of order 20
Quaestiones Mathematicae, 2020Let F be a finite field of characteristic p. There are five non-isomorphic groups of order 20. The structure of U (FD20) is given in [2, 6, 10] and that of U (FQ20) is given in [3, 6], for p = 2, 5...
Sheere Farhat Ansari, Meena Sahai
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Units of Integral Group Rings of Some Metacyclic Groups
Canadian Mathematical Bulletin, 1994AbstractIn this paper, we consider all metacyclic groups of the type 〈a,b | an - 1, b2 = 1, ba = aib〉 and give a concrete description of their rational group algebras. As a consequence we obtain, in a natural way, units which generate a subgroup of finite index in the full unit group, for almost all such groups.
Jespers, Eric +2 more
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2007
Summary: We give a complete characterization of the unit group \(\mathcal U(FS_3)\) of the group algebra \(FS_3\) of the symmetric group \(S_3\) of degree 3 over a finite field \(F\). Moreover, over the prime fields \(\mathbb{Z}_2\) and \(\mathbb{Z}_3\), presentations of the unit groups of the group algebras \(\mathbb{Z}_2S_3\) and \(\mathbb{Z}_3S_3 ...
Sharma, R. K. +2 more
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Summary: We give a complete characterization of the unit group \(\mathcal U(FS_3)\) of the group algebra \(FS_3\) of the symmetric group \(S_3\) of degree 3 over a finite field \(F\). Moreover, over the prime fields \(\mathbb{Z}_2\) and \(\mathbb{Z}_3\), presentations of the unit groups of the group algebras \(\mathbb{Z}_2S_3\) and \(\mathbb{Z}_3S_3 ...
Sharma, R. K. +2 more
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