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The Continuity of Inverse in Groups
Moscow University Mathematics Bulletin, 2022This article is a contribution to the question under which conditions a paratopological group is a topological group. For that the author introduces the concept of a \(\Delta\)-Baire space. A topological space \(X\) is a \(\Delta\)-Baire space if for every set \(P\subseteq X\times X\) containing the diagonal \(\Delta:=\{(x,x):x\in X\}\) and having the ...
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The Complexity of Inversion in Groups
Algebra and Logic, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Representations for the weak group inverse
Applied Mathematics and Computation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dijana Mosic, Predrag S. Stanimirovic
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ON THE GROUP INVERSE FOR THE SUM OF MATRICES
Journal of the Australian Mathematical Society, 2013AbstractLet${ \mathbb{K} }^{m\times n} $denote the set of all$m\times n$matrices over a skew field$ \mathbb{K} $. In this paper, we give a necessary and sufficient condition for the existence of the group inverse of$P+ Q$and its representation under the condition$PQ= 0$, where$P, Q\in { \mathbb{K} }^{n\times n} $.
Bu, Changjiang +3 more
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On the Fundamental Group of Inverse Limits
Bulletin of the Malaysian Mathematical Sciences Society, 2016A set valued function \(f:X\longrightarrow 2^{Y}\) into the nonempty closed subsets of \(Y\) is upper semi-continuous (usc) if for each \(x \in X\) and each open set \(V \subset Y\) containing the set \(f (x)\), there exists an open set \(U\subset X\) such that \(x \in U\) and \(\bigcup_{u\in U} f (u) \subset V\).
Vavpetič, Aleš, Virk, Žiga
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Products of subsets of groups by their inverses
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2013In the paper under review, a group \(G\) is called a \(\mathcal P\)-group (\(\mathcal P_k\)-group for some integer \(k>0\)) if each finite subset \(X\) of \(G\) (each subset \(X\) of size \(|X|\leq k\)) satisfies \(|XX^{-1}|=|X^{-1}X|\). The authors classify all \(\mathcal P\)-groups (in Theorem 7.4) as two infinite families: the abelian groups and ...
Marcel Herzog +3 more
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A generalization of the group inverse
Quaestiones Mathematicae, 2023From the point of view of generalizations, the core inverse of a matrix has received a lot of attention of researchers in this area resulting in many generalizations of the core inverse, like core-EP, DMP, BT, WC and so on. However, the same can not be said for the group inverse.
Ferreyra, D.E., Malik, Saroj B.
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INVERSIONS IN CLASSICAL WEYL GROUPS
Communications in Contemporary Mathematics, 2007We introduce inversions for classical Weyl group elements and relate them, by counting, to the length function, root systems and Schubert cells in flag manifolds. Special inversions are those that only change signs in the Weyl groups of types Bn, Cnand Dn.
Ding, K, Wu, S
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Displacement structure of group inverses
Numerical Linear Algebra with Applications, 2004AbstractA matrix A is said to possess an UV‐displacement structure if rank(AU – VA) is small compared with the rank of A. Estimates for the rank AgV – UAg are presented, where Ag is the group inverse of A. Copyright © 2004 John Wiley & Sons, Ltd.
Yimin Wei 0001, Michael K. Ng 0001
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Individuals, Groups and Inverse Discrimination
Analysis, 1973M ANY morally sensitive people find themselves faced with the following dilemma. On the one hand, they are persuaded by the argument that if being black, e.g., is morally irrelevant, then it is morally irrelevant and no more justifies favourable inverse discrimination than it justifies unfavourable discrimination.
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