Results 151 to 160 of about 17,794,323 (210)
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Publicationes Mathematicae Debrecen, 2007
Let \(FS_m\) denote a group algebra of the symmetric group \(S_m\) of degree \(m\) over a finite field \(F\). In [Acta Math. Acad. Paedagog. Nyházi. (N.S.) 23, No. 2, 129-142 (2007; Zbl 1135.16034)] the authors characterized the unit group \(U(FS_3)\) of \(FS_3\).
Sharma, R. K. +2 more
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Let \(FS_m\) denote a group algebra of the symmetric group \(S_m\) of degree \(m\) over a finite field \(F\). In [Acta Math. Acad. Paedagog. Nyházi. (N.S.) 23, No. 2, 129-142 (2007; Zbl 1135.16034)] the authors characterized the unit group \(U(FS_3)\) of \(FS_3\).
Sharma, R. K. +2 more
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Star-group identities and groups of units
Archiv der Mathematik, 2010This paper is an extension of the authors' [J. Algebra 322, No. 8, 2801-2815 (2009; Zbl 1193.16027)]. Analogously to a star identity in rings with involution a star identity in groups is defined as an element of the free group of countable rank with involution evaluating identically to 1 for elements of a group \(G\) with involution. Suppose that \(G\)
GIAMBRUNO, Antonino +2 more
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On the unit group of a commutative group ring
, 2013We investigate the group of normalized units of the group algebra ℤ_p^e G of a finite abelian p -group G over the ring ℤ_p^e of residues modulo p ^e with e ≥ 1.
V. Bovdi, M. Salim
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GROUP ALGEBRAS WITH ENGEL UNIT GROUPS
Journal of the Australian Mathematical Society, 2016Let $F$ be a field of characteristic $p\geq 0$ and $G$ any group. In this article, the Engel property of the group of units of the group algebra $FG$ is investigated. We show that if $G$ is locally finite, then ${\mathcal{U}}(FG)$ is an Engel group if and only if $G$ is locally nilpotent and $G^{\prime }$ is a $p$-group.
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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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Canadian Mathematical Bulletin, 2000
AbstractLet G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
Farkas, Daniel R., Linnell, Peter A.
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AbstractLet G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
Farkas, Daniel R., Linnell, Peter A.
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Algebraic monoids with affine unit group are affine
, 2006In this short paper we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.
A. Rittatore
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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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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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Formation and Assertion of Data Unit Groups in 3GPP Networks with TSN and PDU Set Support
IEEE Wireless Communications and Networking ConferenceIndustrial applications and Extended Reality vertical sectors have expressed the need for dedicated Quality of Service considerations from 3GPP to support time-sensitive, bursty and high throughput communications.
Sebastian Robitzsch +3 more
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