Non-maximal and disconnected stability groups: SU(3) counter-example to Michel conjecture

1985 ◽  
Vol 154 (2-3) ◽  
pp. 159-165 ◽  
Author(s):  
J. Burzlaff ◽  
T. Murphy ◽  
L. O'Raifeartaigh
Keyword(s):  
Counter Example

scholarly journals Roberts’ weak welfarism theorem: a minor correction

2021 ◽  
Author(s):  
Peter J. Hammond
Keyword(s):  
Euclidean Space ◽  
Social Welfare ◽  
Utility Function ◽  
Weak Continuity ◽  
Strict Preference ◽  
Counter Example ◽  
Independence Of Irrelevant Alternatives ◽  
Unrestricted Domain ◽  
A Minor ◽  
Minor Correction

AbstractRoberts’ “weak neutrality” or “weak welfarism” theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts (Rev Econ Stud 47(2):421–439, 1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors—that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated.

scholarly journals The Annihilation of Space: A Bad (Historical) Concept

2021 ◽  
pp. 1-30
Author(s):  
Alexis D. Litvine
Keyword(s):  
Cultural History ◽  
Intellectual History ◽  
Social History ◽  
Economic Consequences ◽  
Cultural Mediation ◽  
Counter Example ◽  
Dead End ◽  
The Social ◽  
History Of ◽  
Representations Of Space

Abstract This article is a reminder that the concept of ‘annihilation of space’ or ‘spatial compression’, often used as a shorthand for referring to the cultural or economic consequences of industrial mobility, has a long intellectual history. The concept thus comes loaded with a specific outlook on the experience of modernity, which is – I argue – unsuitable for any cultural or social history of space. This article outlines the etymology of the concept and shows: first, that the historical phenomena it pretends to describe are too complex for such a simplistic signpost; and, second, that the term is never a neutral descriptor but always an engagement with a form of historical and cultural mediation on the nature of modernity in relation to space. In both cases this term obfuscates more than it reveals. As a counter-example, I look at the effect of the railways on popular representations of space and conclude that postmodern geography is a relative dead end for historians interested in the social and cultural history of space.

scholarly journals ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

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