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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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 Connections
Associated With
Includes
Source E8 Lattice (Wikipedia)
Source Group Theory (Wikipedia)
Source Group Theory (Wikipedia)
Source Lagrange's Theorem, Group Theory (Wikipedia)
Source Leech Lattice (Wikipedia)
Source Monster Group (Wikipedia)
Sources
1. Group Theory (Wikipedia)
Wikipedialead paragraph
In abstract algebra, group theory studies the algebraic structures known as groups.
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.
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.
View the Source 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 Monster Group (Wikipedia)
E8 Lattice (Wikipedia)
Leech Lattice (Wikipedia)
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