Abelian - Group Theory

Group Theory

  • Abelian group, a group in which the binary operation is commutative
    • Category of abelian groups Ab has abelian groups as objects and group homomorphisms as morphisms
  • Metabelian group is a group where the commutator subgroup is abelian
  • Abelianisation

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Other articles related to "group theory, theory, group, groups":

Combinatorics On Words - Group Theory - Considered Problems
... problem considered in the study of combinatorics on words in group theory is the following for two elements x,y of a semigroup, does x=y modulo the defining relations of x and y ... Undecidable means the theory cannot be proved ... This question asks if a group is finite if the group has a definite number of generators and meets the criteria xn=1, for x in the group ...
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... enjoyed the successes of over one hundred years of study in group theory ... In finite groups, post classification results included the O'Nan–Scott theorem, the Aschbacher classification, the classification of multiply transitive finite ... The modular representation theory entered a new era as the techniques of the classification were axiomatized, including fusion systems, Puig's theory of pairs and ...
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Applications of Group Theory
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History Of Group Theory - Early 19th Century - Convergence
... Group theory as an increasingly independent subject was popularized by Serret, who devoted section IV of his algebra to the theory by Camille Jordan, whose Traité des substitutions et des ... Other group theorists of the 19th century were Bertrand, Charles Hermite, Frobenius, Leopold Kronecker, and Émile Mathieu as well as Burnside, Dickson, Hölder, Moore, Sylow, and Weber ... of the above three sources into a uniform theory started with Jordan's Traité and von Dyck (1882) who first defined a group in the full modern sense ...

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