Branches of Mathematics
Group Theory
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Group theory is the branch of abstract algebra that studies groups, algebraic structures consisting of a set together with an operation that combines any two elements while satisfying closure, associativity, an identity element and invertibility.
Facts
Central QuestionWhat are the finite simple groups, the basic building blocks every finite group is assembled from, and can a complete list of them be proven. 1 Key DebateWhether the classification of finite simple groups, a proof spread across tens of thousands of journal pages by hundreds of authors, can be trusted as complete. A 1983 announcement that the work was finished proved premature once a gap in the quasithin case came to light, and a second-generation proof project has since worked toward a shorter, more checkable version. 2 Cross-Tradition Connections
Sources
1. Group Theory (Wikipedia)
Wikipedialead paragraphQuote, lead paragraph
In abstract algebra, group theory studies the algebraic structures known as groups.
1. Group Theory (Wikipedia)
Wikipediaopening sectionQuote, opening section
One of the most important mathematical achievements of the 20th century was the collaborative effort ... that culminated into a complete classification of finite simple groups.
1. Group Theory (Wikipedia)
WikipediaIncludes: Evariste Galois, History sectionQuote, Includes: Evariste Galois, History section
Evariste Galois coined the term group and established a connection, now known as Galois theory, between the nascent theory of groups and field theory.
2. Classification of Finite Simple Groups (Wikipedia)
WikipediaSecond-generation classification sectionQuote, Second-generation classification section
Daniel Gorenstein announced in 1983 that the finite simple groups had all been classified, but this was premature as he had been misinformed about the proof of the classification of quasithin groups.
Lagrange's Theorem, Group Theory (Wikipedia)
Wikimedia FoundationIncludes: Lagrange's Theorem (Group Theory)View the Source Reader Challenges (0 open reader challenges)
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