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Products of subsets of groups by their inverses
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2013A group \(G\) is called a \(\mathcal P \)-group if each finite subset \(X\) of \(G\) satisfies \(|XX^{-1}|=|X^{-1}X|.\) In this paper we classify all \(\mathcal P \)-groups. This class of groups consists of two infinite families: the abelian groups and the Hamiltonian 2-groups, and of seven small finite groups.
Marcel Herzog +3 more
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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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The group inverse of a companion matrix
Linear and Multilinear Algebra, 1997A complete characterization is given for the group inverse of a companion matrix over an arbitrary ring to exist. Formulae are given for the actual group inverse and some consequences are drawn.
Robert E. Hartwig, Roland Puystjens
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Perturbation Analysis of the Drazin Inverse and the Group Inverse
2018Having studied the perturbation of the M-P inverse and the weighted M-P inverse, we now turn to the perturbation analysis of the Drazin and group inverses.
Yimin Wei, Guorong Wang, Sanzheng Qiao
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On the Fundamental Group of Inverse Limits
Bulletin of the Malaysian Mathematical Sciences Society, 2016In this paper we study the fundamental group of inverse limits, obtained by upper semi-continuous set valued functions. We present a number of crucial examples which demonstrate the technical difficulties, related to the control of the fundamental group in the inverse limit.
Aleš Vavpetič, Žiga Virk
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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} $.
Changjiang Bu +3 more
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The Quarterly Journal of Mathematics, 1941 Inverse shadowing in group actions
Dynamical Systems, 2016ABSTRACTWe study the inverse shadowing property for actions of some finitely generated groups. A tube condition for such actions is introduced and analysed. We prove a reductive inverse shadowing theorem for actions of virtually nilpotent groups.
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Inverses of finite group systems
IEEE Transactions on Automatic Control, 1978Inverse systems are considered for a class of discrete time-invariant systems that include the finite linear sequential circuits (LSC's). Invertibility results for finite group homomorphic sequential systems (FGHSS's), given by Willsky [8], are extended to include systems with throughput A construction is developed for an L -delay inverse of any FGHSS ...
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Inverse semigroups through groups
International Journal of Mathematical Education in Science and Technology, 1990In most introductory abstract algebra courses the topics covered are groups, rings and fields. In recent years, semigroups have been included due to their value in certain areas of computer science. However, after a few examples of familiar semigroups, the subject is forgotten and concentration is placed on developing the group structure. In this paper
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