Search results
Results from the WOW.Com Content Network
A group G is said to be linear if there exists a field K, an integer d and an injective homomorphism from G to the general linear group GL d (K) (a faithful linear representation of dimension d over K): if needed one can mention the field and dimension by saying that G is linear of degree d over K.
In all these cases except for D 4, there is a single non-trivial automorphism (Out = C 2, the cyclic group of order 2), while for D 4, the automorphism group is the symmetric group on three letters (S 3, order 6) – this phenomenon is known as "triality". It happens that all these diagram automorphisms can be realized as Euclidean symmetries ...
In mathematics, a Young tableau (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties.
The classification of finite simple groups says that most finite simple groups arise as the group of k-points of a simple algebraic group over a finite field k, or as minor variants of that construction. Every reductive group over a field is the quotient by a finite central subgroup scheme of the product of a torus and some simple groups.
It's a special week of football so it deserves a special edition of the pod. Sal Vetri joins Matt Harmon to breakdown every fantasy angle from the four games taking place on Thanksgiving and Black ...
The most predictable byproduct of tripling the College Football Playoff from four to 12 teams was that whining would become a varsity sport on its own.. First up was the ACC’s commissioner, Jim ...
A 1 (2) is isomorphic to the symmetric group on 3 points of order 6. A 1 (3) is isomorphic to the alternating group A 4 (solvable). A 1 (4) and A 1 (5) are both isomorphic to the alternating group A 5. A 1 (7) and A 2 (2) are isomorphic. A 1 (8) is isomorphic to the derived group 2 G 2 (3)′. A 1 (9) is isomorphic to A 6 and to the derived ...
Elon Musk and Vivek Ramaswamy, who were tapped by Republican President-elect Donald Trump to lead a new Department of Government Efficiency, have revealed plans to wipe out scores of federal ...