Results 221 to 230 of about 13,095,517 (269)
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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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International Journal of Theoretical Physics, 2004
The authors are interested study of finite effect algebras that arise as intervals in partially ordered abelian groups. They concentrate on semisimple unital groups, which are torsion free and have a finite unit interval. For such a group \(G\), the aditive group homomorphisms \(G \to\mathbb R\) form a directed partially ordered linear space over ...
Foulis, David J., Greechie, Richard J.
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The authors are interested study of finite effect algebras that arise as intervals in partially ordered abelian groups. They concentrate on semisimple unital groups, which are torsion free and have a finite unit interval. For such a group \(G\), the aditive group homomorphisms \(G \to\mathbb R\) form a directed partially ordered linear space over ...
Foulis, David J., Greechie, Richard J.
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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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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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Unital topology on a unital l-group
Mathematica Slovaca, 2020Abstract In this paper we investigate some fundamental properties of unital topology on a lattice ordered group with order unit. We show that some essential properties of order unit norm on a vector lattice with order unit, are valid for unital l-groups.
Pourgholamhossein, Mahmood +1 more
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Unit Groups of Commutative Group Rings
Communications in Algebra, 2006Let \(R\) be a unitary commutative ring and let \(G\) be an Abelian group. In the first part of the paper the authors assume that \(R\) is indecomposable and \(G\) is finite of order invertible in \(R\). They announce a result which describes the decomposition of the group ring \(RG\) into a direct sum of ring extensions of \(R\), in terms of the ...
Mollov, T., Nachev, N.
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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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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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Free groups and involutions in the unit group of a group algebra
Archiv der Mathematik, 2005The authors study the existence of nonabelian free groups in the subgroup generated by the involutions of the unit group of the group algebra \(FG\) over a non-absolute field. If \(\text{char}(F)=p\neq 2\), \(G\) has no \(p\)-elements and the group of units \(U(FG)\) does not contain a nonabelian free subgroup, then the torsion part \(t(G)\) of \(G ...
GIAMBRUNO, Antonino, C. POLCINO MILIES
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