A minimal condition implying a specialK 4-subdivision in a graph

1974 ◽  
Vol 25 (1) ◽  
pp. 210-215 ◽  
Author(s):  
Carsten Thomassen
Keyword(s):  
Minimal Condition

scholarly journals Locally soluble groups with min-n.

1974 ◽  
Vol 17 (3) ◽  
pp. 305-318 ◽  
Author(s):  
H. Heineken ◽  
J. S. Wilson
Keyword(s):  
Soluble Group ◽  
Free Groups ◽  
Torsion Group ◽  
Minimal Condition ◽  
Normal Subgroups ◽  
Soluble Groups ◽  
Isomorphism Classes ◽  
Torsion Groups ◽  
Torsion Free ◽  
General Method

It was shown by Baer in [1] that every soluble group satisfying Min-n, the minimal condition for normal subgroups, is a torsion group. Examples of non-soluble locally soluble groups satisfying Min-n have been known for some time (see McLain [2]), and these examples too are periodic. This raises the question whether all locally soluble groups with Min-n are torsion groups. We prove here that this is not the case, by establishing the existence of non-trivial locally soluble torsion-free groups satisfying Min-n. Rather than exhibiting one such group G, we give a general method for constructing examples; the reader will then be able to see that a variety of additional conditions may be imposed on G. It will follow, for instance, that G may be a Hopf group whose normal subgroups are linearly ordered by inclusion and are all complemented in G; further, that the countable groups G with these properties fall into exactly isomorphism classes. Again, there are exactly isomorphism classes of countable groups G which have hypercentral nonnilpotent Hirsch-Plotkin radical, and which at the same time are isomorphic to all their non-trivial homomorphic images.

scholarly journals Condition for intersection occupation measure to be absolutely continuous

2020 ◽  
Vol 72 (9) ◽  
pp. 1304-1312
Author(s):  
X. Chen
Keyword(s):  
Stochastic Processes ◽  
Lebesgue Measure ◽  
Local Time ◽  
Minimal Condition ◽  
Occupation Measure ◽  
Absolutely Continuous ◽  
Intersection Local Time ◽  
Stationary Increments

UDC 519.21 Given the i.i.d. -valued stochastic processes with the stationary increments, a minimal condition is provided for the occupation measure to be absolutely continuous with respect to the Lebesgue measure on An isometry identity related to the resulting density (known as intersection local time) is also established.

scholarly journals Lie algebras with the minimal condition on centralizer ideals

1989 ◽  
Vol 19 (2) ◽  
pp. 397-407 ◽  
Author(s):  
Falih A. M. Aldosray ◽  
Ian Stewart
Keyword(s):  
Lie Algebras ◽  
Minimal Condition

scholarly journals Groups with the minimal condition on centralizers

1979 ◽  
Vol 60 (2) ◽  
pp. 371-383 ◽  
Author(s):  
Roger M Bryant
Keyword(s):  
Minimal Condition

Joint Attention and the First Person

1998 ◽  
Vol 43 ◽  
pp. 123-136 ◽  
Author(s):  
John Campbell
Keyword(s):  
Joint Attention ◽  
Proper Names ◽  
Minimal Condition ◽  
First Person ◽  
Ordinary Conversation

It is sometimes said that ordinary linguistic exchange, in ordinary conversation, is a matter of securing and sustaining joint attention. The minimal condition for the success of the conversation is that the participants should be attending to the same things. So the psychologist Michael Tomasello writes, ‘I take it as axiomatic that when humans use language to communicate referentially they are attempting to manipulate the attention of another person or persons.’ I think that this is an extremely fertile approach to philosophical problems about meaning and reference, and in this paper I want to apply it to the case of the first person. So I want to look at the case in which you tell me something about yourself, using the first person, and we achieve joint attention to the same object. But I begin with some remarks about how this approach applies to proper names and to perceptual demonstratives.

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