### Some articles on *group, automorphism, automorphism group, automorphisms*:

Automorphisms Of The Symmetric And Alternating Groups - The Exceptional Outer Automorphism of

... Ernst Witt found a copy of Aut(S6) in the Mathieu

*S*_{6}- Other Constructions... Ernst Witt found a copy of Aut(S6) in the Mathieu

**group**M12 (a subgroup T isomorphic to S6 and an element σ that normalizes T and acts by outer**automorphism**) ... The full**automorphism group**of A6 appears naturally as a maximal subgroup of the Mathieu**group**M12 in 2 ways, as either a subgroup fixing a division of the 12 points into a pair of 6-element ... Another way to see that S6 has a nontrivial outer**automorphism**is to use the fact that A6 is isomorphic to PSL2(9), whose**automorphism group**is the projective ...Stable Curve

... it is a complete connected curve whose only singularities are ordinary double points and whose

... it is a complete connected curve whose only singularities are ordinary double points and whose

**automorphism group**is finite ... The condition that the**automorphism group**is finite can be replaced by the condition that it is not of arithmetic genus one and every non-singular rational component meets the other components in at least 3 points (Deli ... one satisfying similar conditions, except that the**automorphism group**is allowed to be reductive rather than finite (or equivalently its connected ...Binary Tetrahedral Group - Properties

... The binary tetrahedral

... The binary tetrahedral

**group**, denoted by 2T, fits into the short exact sequence This sequence does not split, meaning that 2T is not a semidirect product of {±1 ... The binary tetrahedral**group**is the covering**group**of the tetrahedral**group**... Thinking of the tetrahedral**group**as the alternating**group**on four letters, we thus have the binary tetrahedral**group**as the covering**group**, The center of 2T is the subgroup {±1} ...Dynkin Diagram - Automorphisms

... diagrams, some diagrams also have self-isomorphisms or "

... diagrams, some diagrams also have self-isomorphisms or "

**automorphisms**" ... Diagram**automorphisms**correspond to outer**automorphisms**of the Lie algebra, meaning that the outer**automorphism group**Out = Aut/Inn equals the**group**of diagram**automorphisms**... The diagrams that have non-trivial**automorphisms**are An, Dn, and E6 ...Automorphisms Of The Symmetric And Alternating Groups - Small

... For n = 1 and 2, A1 = A2 = 1 is trivial, so the

*n*- Alternating... For n = 1 and 2, A1 = A2 = 1 is trivial, so the

**automorphism group**is also trivial ... For n = 3, A3 = C3 = Z/3 is abelian (and cyclic) the**automorphism group**is GL(1, Z/3*) = C2, and the inner**automorphism group**is trivial (because it ...### Famous quotes containing the word group:

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—Alfred Jarry (1873–1907)

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