In model theory, a stable group is a group that is stable in the sense of stability theory. A group of finite Morley rank is an abstract group G such that the formula x=x has finite Morley rank for the model G. It follows from the definition that the theory of a group of finite Morley rank is ω-stable; therefore groups of finite Morley rank are stable groups.

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dbpprop:abstract
  • In model theory, a stable group is a group that is stable in the sense of stability theory. A group of finite Morley rank is an abstract group G such that the formula x=x has finite Morley rank for the model G. It follows from the definition that the theory of a group of finite Morley rank is ω-stable; therefore groups of finite Morley rank are stable groups. Groups of finite Morley rank behave in certain ways like finite-dimensional objects The striking similarities between groups of finite Morley rank and finite groups are an object of active research.
dbpprop:first
  • A.
  • Alexandre V.
  • Gregory
  • Tuna
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dbpprop:id
  • g/g110270
dbpprop:isbn
  • 978-0-8218-4305-5
dbpprop:last
  • Altinel
  • Borovik
  • Cherlin
  • Pillay
dbpprop:location
  • Providence, R.I.
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dbpprop:reference
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dbpprop:series
  • Mathematical Surveys and Monographs
dbpprop:title
  • Group of finite Morley rank
  • Simple groups of finite Morley rank
dbpprop:volume
  • 145 (xsd:integer)
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dbpprop:year
  • 2008 (xsd:integer)
rdfs:comment
  • In model theory, a stable group is a group that is stable in the sense of stability theory. A group of finite Morley rank is an abstract group G such that the formula x=x has finite Morley rank for the model G. It follows from the definition that the theory of a group of finite Morley rank is ω-stable; therefore groups of finite Morley rank are stable groups.
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  • Stable group
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