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transfinite central series

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  • Central series — In mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, this is an explicit… …   Wikipedia

  • Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… …   Wikipedia

  • Z-group — In mathematics, especially in the area of algebra known as group theory, the term Z group refers to a number of distinct types of groups: * in the study of finite groups, a Z group is a finite groups whose Sylow subgroups are all cyclic. * in the …   Wikipedia

  • Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …   Wikipedia

  • Center (group theory) — In abstract algebra, the center of a group G is the set Z ( G ) of all elements in G which commute with all the elements of G . That is,:Z(G) = {z in G | gz = zg ;forall,g in G}.Note that Z ( G ) is a subgroup of G , because # Z ( G ) contains e …   Wikipedia

  • metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium

  • History of the Church-Turing thesis — This article is an extension of the history of the Church Turing thesis.The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

  • History of the Church–Turing thesis — This article is an extension of the history of the Church–Turing thesis. The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

  • logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

  • number game — Introduction       any of various puzzles and games that involve aspects of mathematics.       Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… …   Universalium

  • Metaphysics — This article is about the branch of philosophy dealing with theories of existence and knowledge. For the work of Aristotle, see Metaphysics (Aristotle). For the occult field, see Metaphysics (supernatural). Philosophy …   Wikipedia

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