Results 251 to 260 of about 148,877 (263)

Group Identities on Symmetric Units

2010
Let F be an infinite field of characteristic different from 2 and G a group. We examine the set of units, \({\mathcal{U}}^{+}(FG)\), symmetric under the natural involution ∗ sending each group element to its inverse. The conditions under which \({\mathcal{U}}^{+}(FG)\) satisfies a group identity are presented, subject to the restriction that G ∕ T is a
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Identities and Inequalities via Symmetrization

1983
The purpose of this survey paper is to examine some specific applications of the process of averaging over finite groups, compact topological groups, and compact homogeneous manifolds. These applications occur in a variety of different disciplines of pure and applied mathematics, such as (i) classical representation theory of finite groups, (ii ...
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Lie Identities on Symmetric Elements

2010
Let F be a field of characteristic different from 2 and G a group. We examine the conditions under which the symmetric elements in FG are Lie nilpotent, bounded Lie Engel, or Lie solvable. For Lie solvability, some restrictions upon G are necessary.
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Power Sum Identities for Arbitrary Symmetric Arrays

SIAM Journal on Applied Mathematics, 1969
Let \([f_n(k)]\), \(k=0,1,\ldots,n\), be an arbitrary symmetric array of numbers in the sense that \(f_n(k)=f_n(n-k)\). A very special case would be the Pascal triangle with \(f_n(k)=\binom{n}{k}\). This paper considers expressions of the general form \(\displaystyle\sum_{k=0}^n k^pf_n(k) = \sum k^pf\), \(p\) an integer, the latter brief symbolism ...
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ANTI-COMMUTATIVE ALGEBRAS WITH SKEW-SYMMETRIC IDENTITIES

Journal of Algebra and Its Applications, 2009
Generalizing Lie algebras, we consider anti-commutative algebras with skew-symmetric identities of degree > 3. Given a skew-symmetric polynomial f, we call an anti-commutative algebra f-Lie if it satisfies the identity f = 0. If sn is a standard skew-symmetric polynomial of degree n, then any s4-Lie algebra is f-Lie if deg f ≥ 4. We describe a free
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Polynomial identities for skew-symmetric matrices

2013
As mentioned in the introduction, Racine and D'Amour have described all identities for Kn, n < 5. In our research we began at n = 5, and immediately found that 8 is the minimal degree, and that there is a large space of identities for degree 8. More precisely, a space of degree 8 multilinear identities for K5 was computed and it has dimension 1756 ...
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Multivariate Symmetric Identities

The Fibonacci Quarterly, 1996
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Symmetric Identities

2009
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Modified Bialternants and Symmetric Function Identities

Journal of the London Mathematical Society, 1950
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Symmetric Units and $$*$$-Identities

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