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A more complex example involves the order of the smallest simple group that is not cyclic. Burnside's p a q b theorem states that if the order of a group is the product of one or two prime powers, then it is solvable, and so the group is not simple, or is of prime order and is cyclic. This rules out every group up to order 30 (= 2 · 3 · 5).
Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on and has a mass gap Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964) , Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975) .
"An Exceptionally Simple Theory of Everything" [1] is a physics preprint proposing a basis for a unified field theory, often referred to as "E 8 Theory", [2] which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything.
The monster was a culmination of the development of sporadic simple groups and can be built from any two of three subquotients: the Fischer group Fi 24, the baby monster, and the Conway group Co 1. The Schur multiplier and the outer automorphism group of the monster are both trivial .
Notably E 6 is the only exceptional simple Lie group to have any complex representations, a requirement for a theory to contain chiral fermions (namely all weakly-interacting fermions). Hence the other four (G 2, F 4, E 7, and E 8) can't be the gauge group of a GUT. [citation needed]
The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge ...
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods ...
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics , which uses experimental tools to probe these phenomena.