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Full-Text Articles in Algebra
Bounds On Squares Of Two-Sets, Dan Slilaty, Jeff Vanderkam
Bounds On Squares Of Two-Sets, Dan Slilaty, Jeff Vanderkam
Mathematical Sciences Technical Reports (MSTR)
For a finite group G, let pi(G) denote the proportion of (x,y) in GxG for which the set {x2,xy,yx,y2} has cardinality i. In this paper we develop estimates on the pi(G) for various i.
Hypergraph Representations And Orders Of Cwatsets, Julie Kerr
Hypergraph Representations And Orders Of Cwatsets, Julie Kerr
Mathematical Sciences Technical Reports (MSTR)
We determine upper bounds on the order of cwatsets of odd order.
When Is The Number Of P-Subgroups Of A Group Satisfying A Property Congruent To 1 (Mod P)?, Jason Fulman, Jeff Vanderkam
When Is The Number Of P-Subgroups Of A Group Satisfying A Property Congruent To 1 (Mod P)?, Jason Fulman, Jeff Vanderkam
Mathematical Sciences Technical Reports (MSTR)
Let T be a property which holds for a group independent of whether or not this group is embedded in a group G or in a p-Sylow subgroup of G. Using a generalization of Sylow's second Theorem, we prove that if for any p-group P the number of subgroups of P satisfying T is congruent to 1 (mod p), then for any group G, the number of p-subgroups satisfying T is also congruent to 1 (mod p). As an application, we give simple proofs of several theorems, including the well-known Frobenius theorem.
The Commutant Of A Certain Compression, William T. Ross
The Commutant Of A Certain Compression, William T. Ross
Department of Math & Statistics Faculty Publications
Let G be any bounded region in the complex plane and K Ϲ G be a simple compact arc of class C1. Let A2(G\K) (resp. A2(G)) be the Bergman space on G\K (resp. G). Let S be the operator multiplication by z on A2(G\K) and C = PN S│N be the compression of S to the semi-invariant subspace N = A2(G\K) Ɵ A2(G). We show that the commutant of C* is the set of all operators …
The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li
The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li
Mathematics & Statistics Faculty Publications
The purpose of this paper is to derive the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations. The Lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp.
The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith
The Kaplansky Test Problems - An Approach Via Radicals, R. Gobel, Brendan Goldsmith
Articles
The existence of non-free, K-free Abelian groups and modules (over some non-left perfect rings R) having prescribed endomorphism algebra is established within ZFC + 0 set theory. The principal technique used exploits free resolutions of non-free R-modules X and is similar to that used previously by Griffith and Eklof; much stronger results than have been obtained heretofore are obtained by coding additional information into the module X. As a consequence we can show, inter alia, that the Kaplansky Test Problems have negative answers for strongly K,-free Abelian groups of cardinality K1 in ZFC and assuming the weak Continuum Hypothesis.